Easy Level Worksheet

Very Short Answer Questions (1 Mark Each)

(1) Write the formula for the curved surface area of a cylinder. Curved surface area = 2πrh13πrh, where r = radius and h = height

Perfect! This covers the lateral surface of the cylinder.

(2) Write the formula for the total surface area of a sphere. Total surface area = 4πr23πr2, where r = radius

Excellent! This covers the entire spherical surface.

(3) What is the volume of a cube of side 3 cm? Volume = cm3

Perfect! Cube volume is always side cubed.

(4) Write the units of volume and surface area. Volume: cm3cm2 (cubic units), Surface area: cm2cm3 (square units)

Excellent understanding of dimensional analysis!

(5) What is the formula for the volume of a cone? Volume = 13πr2h23πr2h, where r = radius and h = height

Correct! Cone volume is one-third of corresponding cylinder.

(6) If the height of a cylinder is doubled, what happens to its volume? Volume becomes times.

Perfect! Volume changes proportionally with height.

(7) Write the formula to find the volume of a hemisphere. Volume = 23πr343πr3, where r = radius

Excellent! Hemisphere is half a sphere's volume.

(8) What is the curved surface area of a cone? Curved surface area = πrl2πrl, where r = radius and l = slant height

Perfect! This covers the conical surface excluding the base.

Short Answer Questions (2 Marks Each)

(1) Find the curved surface area of a cylinder of radius 4 cm and height 10 cm. π cm2

Excellent! Applied the formula correctly.

(2) A cube has an edge of 5 cm. Find its total surface area. Total surface area = cm2

Perfect! Each face has area = edge2.

(3) Find the volume of a hemisphere of radius 7 cm. (Use π = 227).

Volume of hemisphere = cm3 (upto two decimal places)

Excellent calculation with substitution of π value!

(4) A cone has a radius of 3 cm and height 4 cm. Find its volume.

Volume of cone = π cm3

Perfect application of cone volume formula!

(5) Find the total surface area of a sphere of radius 5 cm.

Total surface area of sphere = π cm2

Excellent! Applied sphere surface area formula correctly.

(6) The height and radius of a cylinder are both 7 cm. Find its total surface area.

Total surface area = π cm2

Perfect! Used the complete formula for cylinder surface area.

(7) A cube has a volume of 64 cm3. Find its edge length. Edge = cm

Excellent! Found the cube root correctly.

(8) If the total surface area of a cube is 150 cm2, find the side of the cube. Side = cm

Perfect! Worked backwards from surface area to find the side.

Long Answer Questions (4 Marks Each)

(1) A cylindrical water tank has a radius of 3.5 m and height 5 m. Find the total surface area and volume of the tank. Total Surface Area: = π m2 and Volume: = π m3

Excellent! Complete solution for both surface area and volume.

(2) A cone has a radius of 7 cm and slant height of 25 cm. Find its curved surface area and total surface area. CSA = π cm2 and TSA = π cm2

Perfect! Found both curved and total surface areas systematically.

(3) A hemisphere of radius 10.5 cm is melted and recast into small cones of radius 3 cm and height 4 cm. How many such cones can be made? Number of cones: (Enter whole number)

Therefore, 64 complete cones can be made.

(4) Find the volume and surface area of a solid metallic sphere of radius 6 cm.

V = π cm3

SA = π cm2

Perfect! Complete solution for sphere volume and surface area.

Part B: Objective Questions (1 Mark Each)

Choose the correct answer and write the option (a/b/c/d)

(1) The formula for the volume of a cone is:

(a) πr2h (b) 13πr2h (c) 23πr2h (d) πr2l

Correct! Cone volume is one-third of the corresponding cylinder volume.

(2) The total surface area of a sphere is given by:

(a) 2πr2 (b) 3πr2 (c) 4πr2 (d) πr2

Correct! Sphere surface area formula is 4πr2.

(3) The volume of a cube with edge length a is:

(a) a2 (b) 3a2 (c) a3 (d) 6a2

Correct! Cube volume is edge cubed.

(4) The curved surface area of a cone is:

(a) πr2 (b) πrl (c) 2πrh (d) πr2h

Correct! Cone curved surface area uses radius and slant height.

(5) If the radius of a sphere is doubled, its surface area becomes:

(a) Doubled (b) Tripled (c) Four times (d) Eight times

Correct! Surface area ∝ r², so doubling r gives 4 times the area.

(6) The volume of a cylinder of radius r and height h is:

(a) πr2h (b) 2πr2h (c) πrh2 (d) πr2l

Correct! Cylinder volume is base area times height.

(7) A hemisphere has ? the total surface area of a sphere.

(a) Half (b) One-fourth (c) Three-fourths (d) None of these

Correct! Hemisphere surface = 12×4πr2 + πr2 = 3πr2, which is 34 of sphere's 4πr2.

(8) The total surface area of a cube is 6a2. Then one face of the cube has area:

(a) a2 (b) 6a (c) 3a (d) 2a2

Correct! If total surface area = 6a2, then each face area = 6a26 = a2.

(9) The slant height of a cone is given by:

(a) r2+h2 (b) r2−h2 (c) r + h (d) None

Correct! Using Pythagoras theorem: l2 = r2 + h2.

(10) Volume of a hemisphere is:

(a) 23πr3 (b) 12πr3 (c) 43πr3 (d) πr2h

Correct! Hemisphere volume is half of sphere volume: 12 × 43πr3 = 23πr3.

Basic Mensuration Challenge

Determine whether these statements about basic mensuration are True or False:

Basic Mensuration Quiz