MCQ
Mensuration MCQ - Practice Questions with Answers
Solve 24 Mensuration questions for RAS/RPSC preparation.
Practice questions
Q1If the volumes of two solid spheres stand in the ratio 8 : 27, then the ratio of their surface areas is
Volume scales as r³, so the radius ratio is ∛(8 : 27) = 2 : 3. Surface area scales as r², so the surface-area ratio is 2² : 3² = 4 : 9.
Q2A right circular cone and a hemisphere share the same base radius 7 cm. If the cone's height is 21 cm, find the ratio of the volume of the cone to the volume of the hemisphere.
Volume of the cone = (1/3)π(7)²(21) = 343π. Volume of the hemisphere = (2/3)π(7)³ = (2/3)π × 343 = 686π/3. The required ratio is 343π : (686π/3) = 3 : 2.
Q3Inside a rectangular garden 42 m long and 30 m wide, a path of uniform width 2 m runs along the border. The area of the path alone is:
Outer area = 42 × 30 = 1260 m². Inner rectangle is (42 − 4) by (30 − 4) = 38 × 26 = 988 m². Path area = 1260 − 988 = 272 m².
Q4A brass cylinder of radius 4 cm and height 9 cm is melted and recast into identical spheres each of radius 1.5 cm. The number of complete spheres obtained is
Cylinder volume = πr²h = π × 4² × 9 = 144π cm³. One sphere of radius 1.5 cm has volume (4/3)π(1.5)³ = (4/3)π(3.375) = 4.5π cm³. Number of spheres = 144π / 4.5π = 32.
Q5Workers pack goods in a right triangular prism whose base legs are 8 cm and 15 cm and whose length is 11 cm. What volume does each prism enclose?
Base area of the right triangle = (1/2) × 8 × 15 = 60 cm². Prism volume = base area × length = 60 × 11 = 660 cm³.
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More questions
6A polished metal ball has diameter 14 cm. Taking π = 22/7, its total surface area is
7Two straight stretches of a jogging path measure 100 m each and are joined at both ends by semicircles of diameter 35 m. Taking π = 22/7, one full lap measures:
8A cylindrical oil drum has internal radius 7 cm and height 20 cm. Taking π = 22/7, how many litres of oil can the drum hold?
9A greenhouse tunnel is modelled as a triangular prism. Each triangular end has base 4 m and height 2.5 m, and the tunnel is 18 m long. Find the enclosed volume.
10A cylindrical metal rod of radius 6 cm and length 32 cm is melted and cast into spheres of radius 3 cm. The number of spheres formed is:
11A granite monument is a square pyramid with base edge 20 m and vertical height 21 m. Its volume is:
12A decorative piece has a hemisphere of radius 7 cm surmounted by a cone of the same radius and height 24 cm. Taking π = 22/7, the volume of the piece is:
13A hollow triangular prism with equilateral triangular ends of side 6 cm and length 10 cm is open at both ends. The sheet area required for its three rectangular walls is
14A metal cube of edge 8 cm is melted and recast into smaller cubes of edge 2 cm. How many such smaller cubes are obtained?
15Molten metal from a conical billet (radius 9 cm, altitude 16 cm) completely fills a cylindrical mould of radius 6 cm. How tall must that mould be?