Question

In figure 7.11, a toy made from a hemisphere, a cylinder and a cone is shown. Find the total area of the toy.

Answer 1

For the Cone,

Radius = 3 cm.

Height = 4 cm.

∴ Slant height (l) = √(16+ 9) = √25 = 5

Using the Formula,

Curved surface area of the cone = πrl

= 22/7 × 3 × 5

= 47.14 cm².

For the cylinder,

Radius = 3 cm.

Height = 40 cm.

Curved surface area of the cylinder = 2πrh

= 2 × 22/7 × 3 × 40

= 754.29 cm²

For the Hemisphere,

Radius = 3 cm.

Curved surface area of the hemisphere = 2πr²

= 2 × 22/7 × 3 × 3

= 56.57 cm²

Hence, the total surface area of the Toy = Curved surface area of the cone + Curved surface area of the cylinder + Curved surface area of the hemisphere.

= 47.14 cm² + 754.29 cm² + 56.57 cm²

= 858 cm²

Hope it helps. :-)

Answer 2

Hi ,

1 ) Dimensions of the hemisphere ;

Radius ( r ) = 3 cm

Surface area of the Hemisphere = A1 = 2πr²

2 ) Dimensions of the cylindrical shape ;

Radius ( r ) = 3 cm

Height ( H ) = 40 cm

Surface area of the cylinder ( A2 ) = 2πrH

3 ) Dimensions of the cone shape ;

radius = r = 3 cm

height ( h1 ) = 4 cm

let slant height = l

l = √ r² + h²

l = √ 3² + 4²

l = 5 cm

Surface area of the cone ( A3 ) = πrl

4 ) Total surface area of the toy = A1 + A2 + A3

= 2πr² + 2πrH + πrl

= πr( 2r + 2H + l )

=  22/7 × 3 ( 2×3 + 2×40 + 5 )

= 22/7 × 3 × 91

= 858 cm²

I hope this helps you.

: )