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Solution - A cubical block of side 7 cm is surmounted by a hemisphere. What is the greatest diameter the hemisphere can have? Find the surface area of the solid. - CBSE Class 10 - Mathematics

ConceptSurface Area of a Combination of Solids

Question

A cubical block of side 7 cm is surmounted by a hemisphere. What is the greatest diameter the hemisphere can have? Find the surface area of the solid. [Use π = 22/7]

Solution

From the figure, it can be observed that the greatest diameter possible for such hemisphere is equal to the cube’s edge, i.e., 7cm.

Radius (r) of hemispherical part = 7/2 = 3.5cm

Total surface area of solid = Surface area of cubical part + CSA of hemispherical part − Area of base of hemispherical part

= 6 (Edge)2 + 2πr2 - πr2  = 6 (Edge)2 + πr2

Total surface area of solid = `6(7)^2 + 22/7 xx 7/2xx 7/2`

= 294 + 38.5 = 332.5 cm2

Is there an error in this question or solution?

APPEARS IN

 NCERT Mathematics Textbook for Class 10 (with solutions)
Chapter 13: Surface Areas and Volumes
Q: 4 | Page no. 244

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Reference Material

Solution for question: A cubical block of side 7 cm is surmounted by a hemisphere. What is the greatest diameter the hemisphere can have? Find the surface area of the solid. concept: null - Surface Area of a Combination of Solids. For the course CBSE
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