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Question
There are two identical solid cubical boxes of side 7 cm. From the top face of the first cube a hemisphere of diameter equal to the side of the cube is scooped out. This hemisphere is inverted and placed on the top of the second cube’s surface to form a dome. Find
- the ratio of the total surface area of the two new solids formed
- volume of each new solid formed.
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Solution
First Solid |
Second Solid |
i. Surface Area for first new solid (S1):
6 × 7 × 7 + 2π × 3.52 – π × 3.52
= 294 + 77 – 38.5
= 332.5 cm2
Surface Area for second new solid (S2):
6 × 7 × 7 + 2π × 3.52 – π × 3.52
= 294 + 77 – 38.5
= 332.5 cm2
So S1: S2 = 1 : 1
ii. Volume for first new solid (V1) = `7 xx 7 xx 7 - 2/3 π xx 3.5^3`
= `343 - 539/6`
= `1519/6` cm3
Volume for second new solid (V2) = `7 xx 7 xx 7 + 2/3 π xx 3.5^3`
= `343 + 539/6`
= `2597/6` cm3
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