Class 10 Surface Areas and Volumes (Combinations) — practice questions with answers
Mensuration · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.
1. A cone with a base radius of 5 cm and height of 12 cm is cut by a plane parallel to its base, removing a small cone of height 4 cm from the top. What is the volume of the remaining frustum? (use pi = 3.14)
A302.5 cm³
B200.96 cm³
C314.16 cm³
D150 cm³
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Answer: A) 302.5 cm³
The small cone removed has height 4 cm, so by similar triangles its radius = 5×124=35 cm. Frustum volume = 31×pi×8×(52+5×35+(35)2) = (1/3)*pi*8*36.11 = 302.5 cm³.
2. The largest possible sphere is carved out of a cube of edge 14 cm. What is the radius of this sphere?
A6
B8
C14
D7
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Answer: D) 7
The largest sphere inside a cube has a diameter equal to the edge of the cube. So diameter = 14 cm and radius = 7 cm.
3. A drinking glass is in the shape of a frustum of a cone with end radii 2 cm and 1 cm and vertical height 14 cm. Find its capacity (volume). (use pi = 22/7)
4. A toy is in the shape of a cone mounted on a hemisphere of the same base radius 3.5 cm. The total height of the toy is 15.5 cm. Find the volume of the toy, in cm³. (use pi = 22/7)
A288.75
B243.83
C551.83
D154
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Answer: B) 243.83
The hemisphere contributes its radius 3.5 cm to the total height, so the cone's height = 15.5 - 3.5 = 12 cm. Volume = 31*pi*r²*h + 32*pi*r³ = 154 + 89.83 = 243.83 cm³. Taking 15.5 cm as the cone's height gives 288.75.
5. A juice glass is a cylinder of inner diameter 5 cm and height 10 cm, but its bottom has a hemispherical raised portion of the same radius that reduces the capacity. Find the actual capacity of the glass, in cm³. (use pi = 3.14)