Question

A solid wooden toy is prepared by joining a cone, a cylinder and a sphere, as shown in the given diagram. The radius of each of the three solids is 7 cm and heights of each of the cone and the cylinder is 24 cm. Find:

1. The total surface area of the given solid.
2. The cost of painting the total surface at the rate of ₹ 0.50 per cm². 
   (Use `pi = 22/7`)

Answer 1

(a) Given: Radius of each solid (r) = 7 cm

Height of cone = Height of cylinder = h = 24 cm

Let the slant height of the cone be l.

By formula,

l = `sqrt(r^2 + h^2)`

= `sqrt(7^2 + 24^2)`

= `sqrt(49 + 576)`

= `sqrt(625)`

= 25

Total surface area of sphere = 4πr²

= `4 xx 22/7 xx 7^2`

= `4 xx 22/7 xx 49`

= 616 cm²

Total surface area of cylinder = 2πr(h + r)

= `2 xx 22/7 xx 7 xx (24 + 7)`

= 2 × 22 × 31

= 1364 cm²

Total surface area of cone = πr(r + l)

= `22/7 xx 7 xx (7 + 25)`

= 22 × 32

= 704 cm²

Total surface area of toy = Total surface area of (sphere + cylinder + cone)

= 616 + 1364 + 704

= 2684 cm²

(b) Given: Cost of painting = ₹ 0.50 per cm²

The cost of painting the total surface = 2684 × ₹ 0.50

= ₹ 1,342

Hence, the total cost of painting is ₹ 1,342.