Published by:
CGP EDU Academic Team
Published on: August 14, 2026
The surface area of a cube is increasing at the rate of 2 cm 2 /sec. When its edge is 90 cm, the volume is increasing at the rate of -
Text Solution
Verified by ExpertsThe correct answer is:
D
Let at any time t, the length of each edge of the cube be x cm. Let S denote the surface area and V the volume of the cube. Then,
S = 6x 2 and V = x 3 ⇒ 
= 12 x 
and 
= 3x
2 
⇒ 2 = 12 × 90 
and 
= 3 × 90 2 × 
⇒ 90 × 
= 
and 
= 3 × 90 × 
⇒ 
= 3 × 90 × 
cm 3 /sec = 45 cm 3 /sec.
Hence is the correct answer.
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