100+ Volume and Surface Area Aptitude Questions & Answers - 2

Question: 6

A cone of height 7 cm and base radius cm is carved from a rectangular block of wood 10 cm x 5 cm x 2 cm. the percentage of wood wasted is

(A) 32%

(B) 34%

(D) 54%

View Answer

Ans: B

Volume of the block = (10 × 5 × 2) cm³ = 100 cm³

Volume of the cone carved out = $$({1}/{3} × {22}/{7} × 3 × 3 × 7)$$ cm³ = 66 cm³.

∴ Wood wasted = (100 – 66)% = 34%.

Question: 7

A 4 cm cube is cut into 1 cm cubes. The total surface area of all the small cubes is

(A) 96 cm²

(B) 384 cm²

(D) 824 cm²

View Answer

Ans: B

Number of small cube formed = $$({4 × 4 × 4} / {1 × 1 × 1})$$ = 64.

Total surface area of the small cubes = [64 × (6 × 1²] cm² = 384 cm².

Question: 8

The cost of the paint is Rs. 36.50 per kg. if 1 kg of paint covers 16 square feet, how much will it cost to paint outside of a cube having 8 feet each side?

(A) Rs. 692

(B) Rs. 768

(D) Rs. 876

View Answer

Ans: D

Surface area of the cube = (6 × 8²) sq.ft = 384 sq.ft.

Quantity of paint required = $$({384} / {16})$$ kg = 24 kg.

∴ Cost of painting = Rs. (36.50 × 24) = Rs. 876.

Question: 9

The dimensions of a cuboid are 7 cm, 11 cm and 13 cm. The total surface area is

(A) 311 cm²

(B) 411 cm²

(D) 722 cm²

View Answer

Ans: C

Surface area = [2(7 × 11 + 11 × 13 + 7 × 13)] cm²

= (2 x 311) cm² = 622 cm².

Question: 10

The surface area of a cube is 150 cm². Its volume is

(A) 64 cm³

(B) 94 cm³

(D) 135 cm³

View Answer

Ans: C

6a² = 150 ⇒ a² = 25 ⇒ a = 5.

∴ Volume = a³ = 5³ cm³ = 125 cm³.

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100+ Volume and Surface Area Aptitude Questions & Answers - 2

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