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Question
The frustum shaped outer portion of the table lamp has to be painted including the top part. Find the total cost of painting the lamp if the cost of painting 1 sq.cm is ₹ 2.
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Solution
Slant height of the frustum (l)
= `sqrt("h"^2 + ("R" - "r")^2`
= `sqrt(8^2 + (12 - 6)^2`
= `sqrt(64 + (6)^2`
= `sqrt(64 + 36)`
= `sqrt(100)`
Slant height = 10 m
Total Area to be painted = C.S.A of the Frustum + top area
= πl (R + r) + πr2 sq.units
= π[l (R + r) + r2]
= `22/7[10(12 + 6) + 6^2]`
= `22/7[10 xx 18 + 36] "cm"^2`
= `22/7[180 + 36] "cm"^2`
= `(22 xx 216)/7`
= `4752/7 "cm"^2`
= 678.86 cm2
Cost of painting = ₹ 678.86 × 2 = ₹ 1357.72
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