A toy is in the form of a cylinder with hemisphere ends. If the whole length of the toy is 90 cm and its diameter is 42 cm, find the cost of painting the toy at the rate of 70paise per sq cm.
Toy is in the form of a cylinder with hemisphere ends
Total length of toy = 90 cm
Diameter of toy = 42 cm
Radius of toy = r = 21 cm
Length of cylinder = l = Total length of toy – 2 × Radius of toy
= 90 – 2 × 21 cm = 48 cm
For cost of painting we need to find out the curved surface area of toy
Curved surface area of cylinder = 2πrl
= 2 × 22/7 × 21 × 48 cm2
= 6336 cm2
Curved surface area of hemispherical ends = 2 × 2πr2
= 2 × 2 × 22/7 × 21 × 21 cm2
= 5544 cm2
Surface area of toy = Curved surface area of cylinder + Curved surface area of hemispherical ends
Surface area of toy = 6336 cm2 + 5544 cm2 = 11880 cm2
Cost of painting = Rs 0.70/cm2
Total Cost of painting = Surface area of toy × Cost of painting
= 11880 cm2 × Rs 0.70/cm2 = Rs 8316.00
Total cost of painting the toy = Rs 8316.00