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Draw an isometric sketch for the shape obtained by joining two hemispheres of radius $5 c m$ and then find the surface area and volume of the shape obtained.

Grade: Grade 10

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219.35 c m 2 a n d 423.65 c m 3

256.36 c m 2 a n d 128.45 c m 2

314.15 c m 2 a n d 450.38 c m 3

314.15 c m 2 a n d 523.59 c m 3

answer is D.

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Detailed Solution

Radius of given hemisphere =

5 c m

As, sphere is obtained by adjoining two hemispheres. Therefore its radius will also be the same as the radius of the hemisphere.
Radius of sphere =

5 c m

Also, we know that volume of sphere is given as =

43 π r 3

Substituting value of ‘r’ in above volume formula we have

⇒ V o l u m e (V) = 43 × 227 × (5) 3 ​ ⇒ V o l u m e (V) = 43 × 227 × 5 × 5 × 5 ​ ⇒ V o l u m e (V) = 43 × 227 × 125 ​ ⇒ V o l u m e (V) = 1100021 ​ ⇒ V o l u m e (V) = 523.59

Therefore, we see that volume of sphere of radius

5 c m

523.59 c m 3

.
Now, to find the surface area of the sphere. We use a mensuration formula.
Surface Area =

4 π r 2

Substituting value of ‘r’ in above formula we have,

⇒ S u r f a c e a r e a (A) = 4 × 227 × (5) 2 ​ ⇒ S u r f a c e a r e a (A) = 4 × 227 × 5 × 5 ​ ⇒ S u r f a c e a r e a (A) = 22007 ​ ⇒ S u r f a c e a r e a (A) = 314.15 ​

Therefore, from above we see that the surface area of the sphere is

314.15 c m 2

.
So, the correct Ans is Option 4.

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