The radius of the base of a cone is increasing at the rate of 3 cm/minute and the altitude is decreasing at the rate of 4 cm/minute. The rate of change of lateral surface when the radius = 7 cm and altitude = 24 cm, is -
Text Solution
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Let r, l and h denotes respectively the radius, slant height and height of the cone at any time t. Then,
l 2 = r 2 + h 2 ⇒ 2 l 
= 2r 
+ 2h 
⇒ l 
= r 
+ h 
⇒ l 
= 7 × 3 + 24 × (–4) 
⇒ l 
= –75
Where r = 7 and h = 24, we have
l
2 = 7 2 + 24 2 [ t
2 = r 2 + h 2 ]
⇒ l = 25
∴ l 
= –75 ⇒ 
= – 3
Let S denote the lateral surface area. Then,
⇒ 
= π 
= π 
= π {3 × 25 + 7 × (–3)}
= 54 π cm 2 /min.
Hence is the correct answer.
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