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

1. the ratio of the total surface area of the two new solids formed
2. volume of each new solid formed.

Answer 1

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