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Question
A solid metallic cylinder is cut into two identical halves along its height (as shown in the diagram). The diameter of the cylinder is 7 cm and the height is 10 cm.
Find:
- The total surface area (both the halves).
- The total cost of painting the two halves at the rate of ₹ 30 per cm2 `("Use" π = 22/7)`.
Solution
Here, radius of cylinder (r) = `7/2` cm ...(∴ d = 7 cm)
Height of cylinder = 10 cm
a. T.S.A of a half cylinder
`(πr^2)/2 + (πr^2)/2 + (2πrh)/2 + d xx h`
= `πr^2 + πrh + d xx h`
= `22/7 xx 7/2 xx 7/2 + 22/7 xx 7/2 xx 10 + 7 xx 10`
= `77/2 + 110 + 70`
= `77/2 + 180`
= `(77 + 360)/2`
= `437/2`
= 218.5 cm2
So, total surface area of each half is 218.5 cm2.
b. Cost of painting = Total surface area × Rate of painting
= (218.5 + 218.5) × 30
= ₹ 13,110
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