The total surface area of a right circular cone of height 13cm is90πcm^2 calculate 1) it's radius 2) it's volume (take π 3.14)
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Total surface of the 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
∴ radius = 5 cm
( ii ) Now
h = √ l² - r²
= √ 13² - 5²
= √ 165 - 25
= √ 144
h = 12
Volume⇒⅓πr²h
⇒ ⅓ × 3.14 × 5 × 5 × 12
⇒ 314 cm²
Step-by-step explanation:
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