Question

In Figure 3, a decorative block is shown which is made of two solids, a cube, and a hemisphere. The base of the block is a cube with an edge 6 cm and the hemisphere fixed on the top has a diameter of 4⋅2 cm. Find

(a) the total surface area of the block.
(b) the volume of the block formed. `("Take"  pi = 22/7)`

Answer 1

(a) We need to find the total surface area of the block
Block excludes the base area of hemisphere
The surface area of the block× 

` =  "total surface area of cube + curved surface area of the hemisphere - a base area of hemisphere"`

total surface area of a cube= 6a²; a is a side of a cube

total surface area of cube = 6 × 6² = 216

Base area of hemisphere `pi"r"^2;` base is circular in shape

And curved surface area of hemisphere = `2pi"r"^2`
Total surface area of the block

`216 - pi"r"^2 + 2pi"r"^2`

`= 216 + pi"r"^2`

`= 216 + 22/7 xx ((4.2)/2)^2`

`= 216 + 22/7xx (17.64)/4`

`= 216 + 388.08/28`

`=229.86  "cm"^2`

(b) The volume of the block formed = volume of hemisphere+ volume of a cube

`=2/3 pi"r"^3 + "a"^3`

`= 2/3 xx 22/7 xx((4.2)/2)^2 + 6^3`

`= 2/3 xx 22/7 xx 4.41 + 216`

` = 194.04/21 + 216`

` = 225.24 "cm"^2`