Question

length of a cube shaped solid wooden pieces 14 cm from its top surface some amount of wood is carved out in the shape of a hemisphere with radius 7 cm find the total surface area and volume of corresponding shape ​

Answer 1

Therefore total surface area of the wooden pieces= 1288 cm²

The volume of the shape is  $=\frac{6076}{3}$ cm³

Step-by-step explanation:

Given , length of a cube shape solid wooden pieces 14 cm from its top surface some amount of wood is carved out in the shape of a hemisphere with radius 7 cm.

The surface area of top hemisphere is $2\pi r^2$

                                                               $= 2\times \frac{22}{7} \times 7^2$ cm²

                                                               =308 cm²

The surface area of the remaining wooden block is

$5 l^2$

= $5 \times 14^2$ cm²

=980 cm²

Therefore total surface area of the wooden pieces = (308+980)cm²

                                                                                    =1288 cm²

Again ,

The volume of the hemisphere is $=\frac{2}{3}\times \pi \times r^3$

                                                       $=\frac{2}{3}\times \frac{22}{7} \times 7^3$ cm³

                                                      =$\frac{2156}{3}$ cm²

Total  volume of the wooden piece is = $14^3$ cm³ = 2744 cm³

The volume of the shape =$(2744- \frac{2156}{3})$ cm³

                                         $=\frac{6076}{3}$ cm³