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.
Given, radius r = 7 cm and height h = 24 cm.
Slant height of the cone:
l = √(r² + h²)
⇒ l = √(7² + 24²)
⇒ l = √(49 + 576)
⇒ l = √625 = 25 cm
(a) Total surface area of the sphere = 4πr²
⇒ 4 × \frac{22}{7} × 7² = 616 cm²
Total surface area of the cylinder = 2πr(h + r)
⇒ 2 × \frac{22}{7} × 7 × (24 + 7) = 1364 cm²
Total surface area of the cone = πr(r + l)
⇒ \frac{22}{7} × 7 × (7 + 25) = 704 cm²
Total surface area of the toy = 616 + 1364 + 704 = 2684 cm²
Therefore, the total surface area is 2684 cm².
(b) Cost of painting = 2684 × ₹ 0.50 = ₹ 1342
Therefore, the cost of painting is ₹ 1342.
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