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Class 9 Surface Areas and Volumes — practice questions with answers

Mensuration · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.

1. What is the volume of a cube with side length 3 cm?
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Answer: B) 27 cm³
Volume of a cube is calculated as side length cubed: .
2. Using pi = , the volume of a cylinder is 1540 cm³ and its base radius is 7 cm. Find its height (in cm).
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Answer: B) 10
Volume = pi*r²*h, so 1540 = * 7² * h = * 49 * h = 154h. Therefore h = = 10 cm.
3. Using pi = , find the curved surface area of a cone with base radius 7 cm and slant height 10 cm (in cm²).
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Answer: A) 220
Curved surface area of a cone = pi*r*l = * 7 * 10 = 22 * 10 = 220 cm².
4. Asked for the total surface area of a cuboid measuring 5 cm by 4 cm by 3 cm, a student wrote: Surface area = 2(5 * 4) + 2(4 * 3) = 40 + 24 = 64 cm². What is wrong with this working?
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Answer: A) The pair of 5 cm by 3 cm faces has been left out, so 2(5 * 3) = 30 cm² is missing
A cuboid has THREE pairs of faces, so the total surface area is 2(lb + bh + hl) = 2(20 + 12 + 15) = 2 * 47 = 94 cm squared. The student included only two of the three pairs; the missing pair of 5 cm by 3 cm faces contributes 30 cm squared, and 64 + 30 = 94.
5. A cuboidal water tank measures 2 m by 1.5 m by 1 m. A student says it holds 3 litres because 2 * 1.5 * 1 = 3. What is its correct capacity, in litres? (1 cubic metre = 1000 litres)
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Answer: B) 3000
The multiplication is right but the unit is not: 2 * 1.5 * 1 = 3 CUBIC METRES, not litres. Since 1 cubic metre = 1000 litres, the capacity is 3 * 1000 = 3000 litres.
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