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Class 10 Frustum of a Cone — 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 frustum of a cone is obtained when a cone is cut by a plane that is:
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Answer: A) parallel to its base
When a cone is sliced by a plane parallel to its base and the small top cone is removed, the remaining solid is a frustum.
2. A frustum has radii 10 cm and 4 cm, slant height 10 cm. Its curved surface area (use pi = 3.14), in cm², is:
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Answer: B) 439.6
CSA = pi*l*(R + r) = 3.14*10*(10 + 4) = 3.14*10*14 = 439.6 cm².
3. A frustum-shaped jar has radii 9 cm and 6 cm and height 8 cm.
Find the slant height, then the curved surface area, in cm² (use pi = ).
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Answer: C) 402.79
l = = = = 8.544 cm. CSA = *8.544*(9 + 6) = *8.544*15 = *128.16 = 402.79 cm².
4. The upper part of a metal funnel is a frustum with rim radii 11 cm and 3 cm and a vertical depth of 15 cm. Find the area of sloping sheet in it, in cm². (Take .)
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Answer: B) 748
l = = = 17 cm. CSA = = = 748 cm². 660 uses the depth 15 cm as the slant height; 427.43 uses (R - r) = 8 instead of (R + r) = 14; 1496 doubles the correct answer.
5. A frustum of a cone has end radii 15 cm and 9 cm and a vertical height of 8 cm. Find the slant height of the COMPLETE cone from which it was cut.
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Answer: A) 25 cm
Let the whole cone have height H. By similar triangles , so and H = 20 cm, with base radius 15 cm. Its slant height = = = 25 cm. 10 cm is the FRUSTUM’s slant height ; 20 cm is the whole cone’s height, not its slant; 17 cm pairs the frustum’s height 8 with the base radius 15.
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