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Question
The total surface area of a right circular cone of slant height 13 cm is 90π cm2.
Calculate:
- its radius in cm.
- its volume in cm3. [Take π = 3.14].
Solution
Total surface area of cone = 90π cm2
Slant height (l) = 13 cm
i. Let r be its radius, then
Total surface area = πrl + πr2 = πr(l + r)
∴ πr(l + r) = 90π
`=>` r(13 + r) = 90
`=>` r2 + 13r – 90 = 0
`=>` r2 + 18r – 5r – 90 = 0
`=>` r(r + 18) – 5(r + 18) = 0
`=>` (r + 18)(r – 5) = 0
Either r + 18 = 0, then r = –18 which is not possible
or r – 5 = 0, then r = 5
Therefore, radius = 5 cm
ii. Now
`h = sqrt(l^2 - r^2)`
= `sqrt (13^2 - 5^2)`
= `sqrt (169 - 25)`
= `sqrt(144)`
h = 12 cm
Volume = `1/3pir^2h`
= `1/3 xx 3.14 xx 5 xx 5 xx 12`
= 314 cm3
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