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Chapter 9: Mensuration

    Introduction

    Area of a Polygon

    Solid Shapes

    Surface Area of Cube, Cuboid and Cylinder

    Volume of Cube, Cuboid and Cylinder

    Volume and Capacity

    Exercise 9.1

    Exercise 9.2

    Exercise 9.3

    What Have We Discussed?

    Enhanced Curriculum Support

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Chapter 9: Mensuration > Exercise 9.3

Exercise 9.3

1. Given a cylindrical tank, in which situation will you find surface area and in which situation volume.

Instructions

To find how much water it can hold
Number of cement bags required to plaster it
To find the number of smaller tanks that can be filled with water from it
Volume
Surface Area
Neither

Solution:

(a) The more space a tank has within it, the more water it will hold. Since, this situation pertains to the space occupied by the tank, we need to evaluate the volume.

(b) The plastering is done on the surface of an object. Since, this is regarding the surface of the container, we will work with the the surface area of the tank.

(c) Similar to (a), the more amount of water that it can hold, the more smaller cans will be filled. Since, this is about the holding capacity of the tank, we find work with volume.

2. The diameter of a cylinder (A) is 7 cm with the height being 14 cm. Diameter of cylinder (B) is 14 cm and height is 7 cm.

(a) Without doing any calculations, can you suggest whose volume is greater?

(b) Does the cylinder with the greater volume also have the greater surface area?

Instructions

Compare the radius and height of both cylinders

  • We know that, the volume of a cylinder =
  • From this we can see that, the value of affects the volume of the cylinder more than the . Thus, has a higher volume has it has a
  • Moving on to verifying if a higher volume also gives a higher surface area.
  • Volume of cylinder A = cm3 , cylinder B = cm3
  • Now, we know that the surface area of a cylinder:
  • Therefore, surface area of cylinder A = cm2, cylinder B = cm2
  • Thus, a cylinder with higher volume: a higher surface area.

3. Find the height of a cuboid whose base area is 180 cm2 and volume is 900 cm3.

Instructions

Volume of cuboid=lxbxh

  • We know that the area of the base (from the above formula) is:
  • Substituting the given values.
  • We see that the height is equal to cm.
  • Thus, we have found the required height.

4. A cuboid is of dimensions 60 cm × 54 cm × 30 cm. How many small cubes with side 6 cm can be placed in the given cuboid?

Instructions

Given, Length of cuboid (l) = cm, Breadth of cuboid (b) = cm and Height of cuboid (h) = cm
Thus, Volume of cuboid = lbh = × × = cm3
Volume of cube of side 6 cm = = × × = cm3
So, the Number of Small cubes = (volume of / volume of )
No. of small cubes = / =
Hence, the required number of cubes is 450.

5. Find the height of the cylinder whose volume is 1.54 m3 and diameter of the base is 140 cm ?

Instructions

Given: Volume of cylinder = m3 and diameter of cylinder = cm. Thus, radius (r) = cm
We know: Volume of cylinder =
So, we have: = × × × h
h = 1.54×722×0.7×0.7 =
Hence, the height of the cylinder is 1 m.

6. A milk tank is in the form of cylinder whose radius is 1.5 m and length is 7 m. Find the quantity of milk in litres that can be stored in the tank?

Instructions

Volume of tank = πxr2xh

  • Putting the values in the volume formula.
  • We get volume = m3
  • The capacity of the tank becomes L
  • Capacity of the tank has been found.

7. If each edge of a cube is doubled:

(i) By how many times will its surface area increase ?

(ii) **By how many times will its volume increase ?

Instructions

Let the side length be a

  • We know that the surface area of a cube is:
  • The new side is a’ = 2a which gives: Surface area of new cube =
  • Thus, the new surface area is times of the original area.
  • Moving on to the new volume, we get: Volume of new cube =
  • Thus, the new volume is times of the original volume.

8. Water is pouring into a cubiodal reservoir at the rate of 60 litres per minute. If the volume of reservoir is 108 m3, find the number of hours it will take to fill the reservoir.

Instructions

First, find the rate of water flow

  • Since, 1 L = m3, the rate of water flow = L/min (given) = m3min
  • Further, the rate of water flow per hour = m3hr
  • Now, using the unitary method, we know that 1 m3 will get filled in hours.(Enter number upto two decimal places)
  • Thus, the number of hours taken to fill the reservoir: hours (Round up the result to the nearest whole number)
  • Time taken to fill reservoir has been found.