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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

ConceptArea and Volume of Solids - Cone

#### 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

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#### 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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