Geometry & Mensuration

10 questions available

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All Lines & Angles 20 Triangles 18 Quadrilaterals 3 Circles 7 Perimeter & Area 90 Volume & Surface Area 10
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Q1.A circular cone base radius is R and height is H. If we decrease radius of cone by 20% and increase height by 10%. How much volume will decrease?

Medium
A Decreased by 29.6%
B Decreased by 30.85
C Decreased by 40%
D None of these
Volume & Surface Area PPSC 2026

Correct Answer: A

New volume factor = (0.8)² × 1.1 = 0.704, meaning the volume decreases by 29.6%.

Q2.If a box of cube shape had a volume 2190cm3. Its one side area will be?

Medium
A 169 cm 3
B 170 cm 3
C 171 cm 3
D None of these
Volume & Surface Area PPSC 2026

Correct Answer: C

Per the answer key, the surface area of one side of the cube works out to 171 cm².

Q3.If the volume of a cube is 343m3,then then find the area of one side:

Medium
A 43m2
B 49m2
C 51m2
D 57m2
Volume & Surface Area PPSC 2026

Correct Answer: B

Side of cube = ∛343 = 7m. Area of one face = 7² = 49 m².

Q4.If the radius of cone is 10cm and height is 30find he volume of cone?

Medium
A 500π cm3
B 2000π cm3
C 1000π cm3
D 3000π cm3
Volume & Surface Area PPSC 2026

Correct Answer: C

Volume of cone = 1/3 πr²h = 1/3 × π × 100 × 30 = 1000π cm³.

Q5.The Volume of a cube is 64cm3 which is painted, find its surface area?

Hard
A 95cm2
B 96cm2
C 97cm2
D None of these
Volume & Surface Area PPSC 2026

Correct Answer: B

Q6.A water tank in the shape of a cuboid has length 1.5 metres and width 1.0 metre. How many litres of water are in the tank if the water is 60 centimetres deep?

Medium
A 9000 litres
B 900 litres
C 90 litres
D None of these
Volume & Surface Area CSS 2026

Correct Answer: B

Volume = 1.5 x 1.0 x 0.6 = 0.9 m³ = 900 litres.

Q7.What is the total surface area of a cylinder having a radius of 3.5 cm and height 5.5 cm?

Medium
A 211.5 sq cm
B 198 sq cm
C 121 sq cm
D None of these
Volume & Surface Area CSS 2026

Correct Answer: B

Total surface area of a cylinder = 2πr(r+h) = 2π(3.5)(3.5+5.5) ≈ 198 sq cm.

Q8.The volume of a cylinder is to be calculated using the formula V = πr²L. If the radius (r) is 3 cm and the length (L) is 10 cm, what is the volume?

Medium
A 90π cm³
B 100π cm³
C 120π cm³
D 75π cm³
Volume & Surface Area PPSC

Correct Answer: A

V = π × r² × L = π × 3² × 10 = π × 9 × 10 = 90π cm³.

Q9.The volume of a cone is 245π cm³ and its radius is 7 cm. Find its height?

Medium
A 15 cm
B 10 cm
C 7 cm
D 6 cm
Volume & Surface Area PPSC

Correct Answer: A

Volume of a cone = (1/3)πr²h. Substituting the known values: 245π = (1/3)π × 7² × h => 245 = (49/3)h => h = (245 × 3) / 49 = 5 × 3 = 15 cm.

Q10.The volume of a rectangular solid is 1,440 cubic inches. If the height is 3 inches, what could be its length and width?

Medium
A 4 inches by 10 inches
B 8 inches by 20 inches
C 10 inches by 48 inches
D 30 inches by 40 inches
Volume & Surface Area PPSC

Correct Answer: C

Volume = length × width × height. Since height is 3: Volume = length × width × 3 = 1440. Thus, length × width = 480. Among the options, 10 inches by 48 inches gives 10 × 48 = 480.