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Question
The radii of the circular ends of a solid frustum of a cone are 33 cm and 27 cm, and its slant height is 10 cm. Find its capacity and total surface area.
Solution
Greater radius = R = 33 cm
Smaller radius = r = 27 cm
Slant height = l = 10 cm
Using the formula for height of a frustum:
Height = h =
`=sqrt(l^2-(R-r)^2)`
`=sqrt(10^2-(33-27)^2)`
`=sqrt(100-(6)^2)`
`=sqrt(100-36)`
`=sqrt(64)=8 "cm"`
Capacity of the frustum
`= 1/3pi"h"("R"^2+r^2+"Rr")`
`= 1/3xx22/7xx8(33^2+27^2+33xx27)`
`=(22xx8)/(3xx7)xx2709 = 22704 "cm"^3`
Surface area of the frustum
= πR2 + πr2 + πl(R + r)
= π [R2 + r2 +(R + r)]
`=22/7 [33^2 + 27^2 + 10(33+27)] `
`=22/7[1089 + 729 + 10(60)]`
`=(22xx2418)/7 = 7599.43 "cm"^2`
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