Enhanced Curriculum Support

SecA

1. Two identical solid hemispheres of equal base radius r cm are stuck together along their bases. The total surface area of the combination is 6πr2.

2. In a right circular cone, the cross-section made by a plane parallel to the base is a

3. A solid ball is exactly fitted inside the cubical box of side a. The volume of the ball is 43πa3.

4. An open metallic bucket is in the shape of a frustum of a cone, mounted on a hollow cylindrical base made of the same metallic sheet. The surface area of the metallic sheet used is equal to curved surface area of frustum of a cone + area of circular base + curved surface area of cylinder.

SecB

1. A solid cylinder of radius r and height h is placed over other cylinder of same height and radius. The total surface area of the shape so formed is 4πrh + 4πr2.

2. A solid cone of radius r and height h is placed over a solid cylinder having same base radius and height as that of a cone The total surface area of thecombined solid is

3. Three metallic solid cubes whose edges are 3 cm, 4 cm and 5 cm are melted and formed into a single cube. Find the edge of the cube so formed.

4. How many shots each having diameter 3 cm can be made from a cuboidal lead solid of dimensions 9 cm x 11 cm x 12 cm?

5. A bucket is in the form of a frustum of a cone and holds 28.490 L of water. The radii of the top and bottom are 28 cm and 21 cm, respectively. Find the height of the bucket.

6. The rain water from a roof of dimensions 22 m x 20 m drains into a cylindrical vessel having diameter of base 2 m and height 3.5 m. If the rain water collected from the roof just fill the cylindrical vessel, then find the rainfall (in cm).

SecC

1. Two solid cones A and B are placed in a cylindrical tube as shown in the figure. The ratio of their capacities is 2 : 1. Find the heights and capacities of cones. Also, find the volume of the remaining portion of the cylinder.

2. Marbles of diameter 1.4 cm are dropped into a cylindrical beaker of diameter 7 cm containing some water. Find the number of marbles that should be dropped into the beaker, so that the water level rises by 5.6 cm.

3. How many spherical lead shots each of diameter 4.2 cm can be obtained from a solid rectangular lead piece with dimensions 66 cm, 42 cm and 21 cm?

4. How many spherical lead shots of diameter 4 cm can be made out of a solid cube of lead whose edge measures 44 cm.

5. The barrel of a fountain pen, cylindrical in shape, is 7 cm long and 5 mm in diameter. A full barrel of ink in the pin is used up on writing 3300 words on an average. How many words can be written in a bottle of ink containing one-fifth of a litre?

6. Water flows through a cylindrical pipe, whose inner radius is 1 cm, at the rate of 80 cms-1 in an empty cylindrical tank, the radius of whose base is 40 cm. What is the rise of water level in tank in half an hour?

SecD

1. A wall 24 m long, 0.4 m thick and 6 m high is constructed with the bricks each of dimensions 25 cm x 16 cm x 10 cm. If the mortar occupies 16 th of the volume of the wall, then find the number of bricks used in constructing the wall.

2. Find the number of metallic circular disc with 1.5 cm base diameter and of height 0.2 cm to be melted to form a right circular cylinder of height 10 cm and diameter 4.5 cm.

3. How many cubic centimetres of iron is required to construct an open box whose external dimensions are 36 cm, 25 cm and 16.5 cm provided the thickness of the iron is 1.5 cm. If one cubic centimetre of iron weights 7.5 g, then find the weight of the box.

4. A factory manufactures 120000 pencils daily. The pencils are cylindrical in shape each of length 25 cm and circumference of base as 1.5 cm. Determine the cost of colouring the curved surfaces of the pencils manufactured in one day at ₹ 0.05 per dm2

5. Water is flowing at the rate of 15 kmh-1 through a pipe of diameter 14 cm into a cuboidal pond which is 50 m long and 44 m wide. In what time will the level of water in pond rise by 21 cm?

6. A pen stand made of wood is in the shape of a cuboid with four conical depressions and a cubical depression to hold the pens and pins, respectively. The dimensions of cubiod are 10 cm, 5 cm and 4 cm. The radius of each of the conical depressions is 0.5 cm and the depth is 2.1 cm. The edge of the cubical depression is 3 cm. Find the volume of the wood in the entire stand.

SecE

1. A solid iron cuboidal block of dimensions 4.4 m x 2.6m x lm is recast into a hollow cylindrical pipe of internal radius 30 cm and thickness 5 cm. Find the length of the pipe.

2. 500 persons are taking a dip into a cuboidal pond which is 80 m long and 50 m broad. What is the rise of water level in the pond, if the average displacement of the water by a person is 0.04 m3?

3. A milk container of height 16 cm is made of metal sheet in the form of a frustum of a cone with radii of its lower and upper ends as 8 cm and 20 cm, respectively. Find the cost of milk at the rate of ? 22 per L which the container can hold.

4. A cylindrical bucket of height 32 cm and base radius 18 cm is filled with sand. This bucket is emptied on the ground and a conical heap of sand is formed. If the height of the conical heap is 24 cm, find the radius and slant height of the heap.

5. A rocket is in the form of a right circular cylinder closed at the lower end and surmounted by a cone with the same radius as that of the cylinder. The diameter and height of the cylinder are 6 cm and 12 cm, respectively. If the slant height of the conical portion is 5 cm, then find the total surface area and volume of the rocket, (use π = 3.14)

6. A solid right circular cone of height 120 cm and radius 60 cm is placed in a right circular cylinder full of water of height 180 cm. Such that it touches the bottom. Find the volume of water left in the cylinder, if the radius of the cylinder is equal to the radius to the cone.

Problem1

Situation: A local park is planning to install new benches and tables made from recycled materials. Each bench has a rectangular surface area of 1.5 m², while each table has a circular surface area of 1.2 m².

1. If the park wants to install 5 benches and 3 tables, what is the total surface area needed for these installations?

2. How does using recycled materials contribute to environmental sustainability?

Problem2

Situation: A community garden project involves constructing a cylindrical water tank to store rainwater. The tank has a radius of 0.75 m and a height of 2 m.

1. Calculate the volume of the tank. Discuss the importance of rainwater harvesting for sustainable agriculture.

Problem3

Situation: A company is designing a new packaging box for their product. The box is in the shape of a rectangular prism with dimensions 30 cm x 20 cm x 15 cm.

1. What is the surface area of the box?

2. Why is it important for companies to consider surface area in packaging design, especially in reducing material waste?

Problem4

Situation: A sports store sells a spherical basketball with a diameter of 24 cm..

1. Calculate the volume of the basketball. Reflect on how understanding volume is crucial in manufacturing sports equipment for optimal performance.

Problem5

Situation: A family is renovating their home and wants to paint the walls of a rectangular room measuring 5 m x 4 m with a height of 3 m. They plan to leave the area of the windows (1.5 m²) unpainted.

1. Calculate the total surface area of the walls that need to be painted. Discuss the importance of careful planning in home renovations to save costs and resources.

Q1

1. A circular garden with a radius of 5 m is surrounded by a path of uniform width, making the total area of the garden plus path equal to 100 m². Determine the width of the path.

2. How does this exercise illustrate the importance of area in landscape design?

Q2

1. A water tank is in the shape of a cone with a base radius of 3 m and a height of 4 m. If water is being filled at a rate of 5 liters per minute, how long will it take to fill the tank completely?

Q3

1. Two different shapes are being considered for a playground slide: a rectangular prism and a half-cylinder. If both have the same height and the rectangular slide has a length of 4 m and a width of 1 m, which slide offers more surface area for painting?

2. Justify your reasoning with calculations.

Q4

1. Imagine you are designing a new sports facility that includes a cylindrical swimming pool with a diameter of 10 m and a depth of 2 m. How would the design change if you needed to add a shallow area for children?

2. Calculate the new volume if the shallow area is 1 m deep and has a radius of 3 m. Discuss the importance of safety in your design.

Q5

1. A factory produces containers in the shape of a cube and a sphere. The volume of both containers is the same. If the cube has a side length of 5 cm, which container has a smaller surface area?

2. Explain the significance of this in terms of material usage and cost.

Questions

1. A mason constructs a wall of dimensions 270 cmx 300 cm x 350 cm with the bricks each of size 22.5 cm x 11.25 cmx 8.75 cm and it is assumed that 18 space is covered by the mortar. Then, the number of bricks used to construct the wall is

2. Twelve solid spheres of the same size are made by melting a solid metallic cylinder of base diameter 2 cm and height 16 cm. The diameter of each sphere is

3. The radii of the top and bottom of a bucket of slant height 45 cm are 28 cm and 7 cm, respectively. The curved surface area of the bucket is

4. A medicine-capsule is in the shape of a cylinder of diameter 0.5 cm with two hemispheres stuck to each of its ends. The length of entire capsule is 2 cm. The capacity of the capsule is

5. If two solid hemispheres of same base radius r are joined together along their bases, then curved surface area of this new solid is

6. During conversion of a solid from one shape to another, the volume of the new shape will

7. The diameters of the two circular ends of the bucket are 44 cm and 24 cm. The height of the bucket is 35 cm. The capacity of the bucket is

8. If volumes of two spheres are in the ratio 64 : 27, then the ratio of their surface areas is

9. A cone of radius 8 cm and height 12 cm is divided into two parts by a plane through the mid-point of its axis parallel to its base. Find the ratio of the volumes of two parts.

10. Two identical cubes each of volume 64 cm3 are joined together end to end. What is the surface area of the resulting cuboid?

11. From a solid cube of side 7 cm, a conical cavity of height 7 cm and radius 3 cm is hollowed out. Find the volume of the remaining solid.

12. Two cones with same base radius 8 cm and height 15 cm are joined together along their bases. Find the surface area of the shape so formed.

13. solid metallic hemisphere of radius 8 cm is melted and recasted into a right circular cone of base radius 6 cm. Determine the height of the cone.

14. A hemispherical bowl of internal radius 9 cm is full of liquid. The liquid is to be filled into cylindrical shaped bottles each of radius 1.5 cm and height 4 cm. How many bottles are needed to empty the bowl?

Question 1

Abhishek wanted to make a cottage at his farm house and brought a design from an architect which looks like a cuboid surmounted a pyramid. The base of the house is in a cuboidal shape whereas the roof is a rectangular based pyramid. He decided to do all the civil work in his own supervision and accordingly planned to make the walls with bricks and roof with GI sheets. The dimension of cuboidal portion of the house is decided to be 20feet length,15 feet wide and 10 feet height with thickness of the walls 1 feet where there are 2 doors of each 6feet ×3feet and 2 windows each 4 feet ×3 feet.

Based on your understanding of the above case study, answer all the five questions below

1. If the wall of the cottage will be made by bricks and cement mortar where 110 th of the volume will be used by the mortar and rest by bricks of dimension, find the number of required bricks?

2. If one bag cement of 40 kg used to plaster a surface area of 100 square feet, then how many bags of cement will be required for plastering the walls on both sides leaving the doors and windows and their edges.

3. If the floor of the cottage has to paved with tiles of rhombus shaped with diagonals 2 feet & 1 feet, then how many tiles will be required for the floor with extra 10 % for wastage?

4. If some cartons of size 2 feet x 2 feet x 1 feet are to be kept inside the house up to a height of 6 feet then what is the maximum number of cartons can be kept inside the cottage?

5. If the builder got a contract to construct the building with a cost of Rs 100 per cubic feet volume and the volume of pyramidal portion is 800 cubic feet, what will be the approximate cost he needs to spend in the construction?

Sol

(1) Bricks required = 11200

(2) Cement bags required = 18

(3) Tiles required = 1100

(4) Maximum cartons = 90

(5) Total cost = ₹1,80,000

Question 2

Villagers of Shyampur decided to have a park for children and their inhabitants so they chose a circular field of radius 35 metre at the end of their village. Planned to have a fountain at the centre and four roads from the fountain to the boundary as given in the figure. The roads are creating right angle between the adjacent roads. They collected the soil dug out from the fountain well at the centre and used them to spread on the four equal roads.

Based on your understanding of the above case study, answer all the five questions below:

1. If the well for fountain is dug with diameter 3.5 m and 7-meter-deep then find the amount of soil would be taken out from it?

2. What will be the area left for plantation and lawn?

3. If the soil taken out has to spread over four roads each of length at edge 33 meter then find how much height the roads will be due to the soils spreading?

4. What is the ratio of the areas used for lawn with respect to the total area of the land?

5. Find the area left for the lawn and roads except the fountain well?

Sol

(1) Soil taken out = 67.375 m3

(2) Area left for plantation and lawn = 3739.75 m2

(3) Height of roads = 0.512 m

(4) Ratio of lawn area to total area = 0.974

(5) Area left for lawn and roads except fountain well = 3767.75 m2