Question

A solid wooden toy is in the shape of a cone surmounted on a hemisphere of the same radius 2.1 cm. If the total height of the wooden toy is 8.1cm, find its total surface area and volume.​

Answer 1

Step-by-step explanation:

Volume of the toy = Volume of the hemispherical part + Volume of conical part

Volume of a hemisphere of radius 'r' =

3

2

πr

3

Volume of a cone =

3

1

πr

2

h where r

is the radius of the base of the cone and h is the height.

The hemisphere and the cone will have the same radius r =4.2cm

Since total length of the toy is 10.2 cm, the length of the conical part will be 10.2−4.2=6cm

Hence, Volume of the solid =(

3

2

×

7

22

×4.2

3

)+(

3

1

×

7

22

×4.2

2

×6)=266.112cm

3