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A Cubical Block of Side 7 Cm is Surmounted by a Hemisphere of the Largest Size. Find the Surface Area of the Resulting Solid. - ICSE Class 10 - Mathematics

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Question

A cubical block of side 7 cm is surmounted by a hemisphere of the largest size. Find the surface area of the resulting solid. 

Solution

The diameter of the largest hemisphere that can be placed on a face of a cube of side 7 cm will be 7 cm. 

Therefore, radius=`r=7/2cm` 

Its curved surface area=`2pir^2` 

`=2xx22/7xx7/2xx7/2` 

`=77 cm^2`  ......................(1)

 Surface area of the top of the resulting solid = Surface area of the top face of the cube − Area of the base of the hemisphere 

=`(7xx7)-(22/7xx49/4)` 

`=49-77/2` 

`=(98-77)/2` 

`=21/2` 

`= 10.5 cm^2`....................(2) 

Surface area of the cube`=5xx("side")^2=5xx49=245 cm^2` 

Total area of resulting solid`=245+10.5+77=332.5 cm^2` 

  Is there an error in this question or solution?

APPEARS IN

 Selina Solution for Selina ICSE Concise Mathematics for Class 10 (2020 to Current)
Chapter 20: Cylinder, Cone and Sphere
Exercise 20(E) | Q: 4 | Page no. 311
Solution A Cubical Block of Side 7 Cm is Surmounted by a Hemisphere of the Largest Size. Find the Surface Area of the Resulting Solid. Concept: Area and Volume of Solids - Cone.
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