Moderate Level Worksheet

Very Short Answer Questions (1 Mark Each)

(1) Find the volume of a cube whose side is 12 cm.

Correct! Volume = 123 = 12 × 12 × 12 = 1728 cm3.

(2) Find the total surface area of a cuboid with dimensions 8 cm × 5 cm × 3 cm.

Perfect! TSA = 2(lb + bh + hl) = 2(40 + 15 + 24) = 2(79) = 158 cm2.

(3) Find the lateral surface area of a cylinder with radius 7 cm and height 14 cm.

Excellent! LSA = 2πrh = 2π × 7 × 14 = 196π ≈ 616 cm2.

(4) Find the volume of a cone with radius 3 cm and height 9 cm.

Great! Volume = 13πr2h = 13π × 9 × 9 = 27π ≈ 84.78 cm3.

(5) The radius of a sphere is 5 cm. Find its surface area.

Correct! Surface area = 4πr2 = 4π × 25 = 100π ≈ 314 cm2.

Short Answer Questions (2 Marks Each)

Answer each question with detailed calculations

(1) A cube has side 10 cm. Find its lateral surface area and total surface area.

LSA: cm2 TSA: cm2

Excellent! LSA = 4a2 = 4 × 100 = 400 cm2, TSA = 6a2 = 6 × 100 = 600 cm2.

(2) A cylinder has radius 6 cm and height 10 cm. Find its volume and total surface area.

Volume: cm3 TSA: cm2

Perfect! Volume = πr2h = π × 36 × 10 ≈ 1130.4 cm3, TSA = 2πr(r + h) = 2π × 6 × 16 ≈ 602.88 cm2.

(3) A cone has radius 4 cm and height 9 cm. Find its slant height and lateral surface area.

Slant height: cm LSA: cm2

Correct! Slant height = 42+92 = 97 ≈ 9.85 cm, LSA = πrl = π × 4 × 9.85 ≈ 123.7 cm2.

(4) A cuboid has dimensions 12 cm × 6 cm × 8 cm. Find its volume and lateral surface area.

Volume: cm3 LSA: cm2

Great! Volume = 12 × 6 × 8 = 576 cm3, LSA = 2h(l + b) = 2 × 8 × (12 + 6) = 288 cm2.

(5) The diameter of a sphere is 14 cm. Find its volume and surface area.

Volume: cm3 Surface area: cm2

Perfect! Radius = 7 cm. Volume = 43πr3 = 43π × 343 ≈ 1436.03 cm3, Surface area = 4πr2 = 4π × 49 ≈ 615.44 cm2.

Long Answer Questions (4 Marks Each)

(1) A cuboid has length 15 cm, breadth 10 cm, and height 8 cm. Find its volume, lateral surface area, and total surface area.

Volume: cm3 LSA: cm2 TSA: cm2

Correct! Volume = 15 × 10 × 8 = 1200 cm3, LSA = 2h(l + b) = 2 × 8 × 25 = 400 cm2, TSA = 2(150 + 80 + 120) = 700 cm2.

(2) A cylinder has radius 10 cm and height 21 cm. Find its slant height if it is cut along a vertical line and rolled into a cone with the same base radius.

Slant height: cm

(3) A cone has base radius 7 cm and slant height 25 cm. Find its lateral surface area, total surface area, and volume.

LSA: cm2 TSA: cm2 Volume: cm3

Excellent! Height = 252−72 = 576 = 24 cm. Use this value to calculate the respective areas.

(4) A sphere has radius 12 cm. Find the volume of the sphere and the curved surface area of the largest hemisphere formed from it.

Sphere volume: cm3 Hemisphere surface area: cm2

Great! Sphere volume = 43πr3 = 43π × 1728 ≈ 7234.56 cm3. Hemisphere curved surface area = 2πr2 = 2π × 144 ≈ 904.32 cm2.

(5) A metallic solid cube of side 10 cm is melted to form smaller cubes of side 2 cm each. Find the number of smaller cubes formed and the surface area of one smaller cube.

Number of cubes: Surface area of one small cube: cm2

Correct! Large cube volume = 1000 cm3, small cube volume = 8 cm3. Number = 10008 = 125. Surface area of small cube = 6 × 22 = 24 cm2.

Part B: Objective Questions (1 Mark Each)

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

(1) The volume of a cube with side 8 cm is:

(a) 512 cm3 (b) 64 cm3 (c) 128 cm3 (d) 256 cm3

Correct! Volume = 83 = 8 × 8 × 8 = 512 cm3.

(2) The lateral surface area of a cylinder with radius 5 cm and height 12 cm is:

(a) 120π cm2 (b) 100π cm2 (c) 110π cm2 (d) 130π cm2

Correct! LSA = 2πrh = 2π × 5 × 12 = 120π cm2.

(3) The volume of a cone with radius 3 cm and height 12 cm is:

(a) 36π cm3 (b) 36π3 cm3 (c) 36π2 cm3 (d) 48π cm3

Correct! Volume = 13πr2h = 13π × 9 × 12 = 36π cm3.

(4) The total surface area of a cube with side 9 cm is:

(a) 324 cm2 (b) 243 cm2 (c) 216 cm2 (d) 486 cm2

Wait, let me recalculate: TSA = 6 × 92 = 6 × 81 = 486 cm2.

(5) The radius of a sphere is 7 cm. Its volume is:

(a) 1436 cm3 (b) 1435 cm3 (c) 1434 cm3 (d) 1440 cm3

Correct! Volume = 43πr3 = 43π × 343 = 1372π3 ≈ 1437 cm3.

(6) The lateral surface area of a cone with radius 5 cm and slant height 13 cm is:

(a) 65π cm2 (b) 60π cm2 (c) 70π cm2 (d) 75π cm2

Correct! LSA = πrl = π × 5 × 13 = 65π cm2.

(7) A cylinder has radius 6 cm and height 14 cm. Its total surface area is:

(a) 628 cm2 (b) 616 cm2 (c) 600 cm2 (d) 754 cm2

Correct! TSA = 2πr(r + h) = 2π × 6 × 20 = 240π ≈ 754 cm2.

(8) The slant height of a cone with radius 9 cm and height 12 cm is:

(a) 15 cm (b) 14 cm (c) 13 cm (d) 16 cm

Correct! Slant height = r2+h2 = 81+144 = 225 = 15 cm.

(9) A cuboid has base 6 cm × 4 cm and height 10 cm. Its lateral surface area is:

(a) 200 cm2 (b) 180 cm2 (c) 160 cm2 (d) 140 cm2

Correct! LSA = 2h(l + b) = 2 × 10 × (6 + 4) = 20 × 10 = 200 cm2.

(10) A cube of side 12 cm is melted to form smaller cubes of side 3 cm. The number of smaller cubes is:

(a) 64 (b) 72 (c) 48 (d) 60

Correct! Large cube volume = 123 = 1728 cm3, small cube volume = 33 = 27 cm3. Number = 172827 = 64.

Advanced 3D Geometry Challenge

Determine whether these statements are True or False:

Advanced 3D Geometry Quiz