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 :

(a) the total surface area of the given solid.

(b) the cost of painting the total surface at the rate of ₹ 0.50 per cm².

(a) Given,

Radius of each solid (r) = 7 cm

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

Let slant height of cone be l.

By formula,

$l = \sqrt{r^2 + h^2} \\[1em] = \sqrt{7^2 + 24^2} \\[1em] = \sqrt{49 + 576} \\[1em] = \sqrt{625} \\[1em] = 25.$

Total surface area of sphere = 4πr²

= 4 × $\dfrac{22}{7}$ × 7²

= 616 cm².

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

= 2 × $\dfrac{22}{7}$ × 7 × (24 + 7)

= 2 × 22 × 31

= 1364 cm².

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

= $\dfrac{22}{7}$ × 7 × (7 + 25)

= 22 × 32

= 704 cm²

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

= 616 + 1364 + 704

= 2684 cm².

Hence, total surface area of toy = 2684 cm².

(b) Given,

Cost of painting = ₹ 0.50 per cm².

The cost of painting the total surface = 2684 × ₹ 0.50 = ₹ 1,342

Hence, total cost of painting = ₹ 1,342.