Question

Diameter of a sphere is 32(2x + 5), the rate of change of its surface area with respect to x is​

Answer 1

Step-by-step explanation:

Answer

The volume of a sphere (V) with radius (r) is given by,

V=

3

4

πr

3

It is given that,

d=

2

3

(2x+1)

∴r=

4

3

(2x+1)

∴V=

3

4

π(

4

3

)

3

(2x+1)

3

=

16

9

π(2x+1)

3

Hence, the rate of change of volume with respect to x is given as,

dx

dV

=

16

9

π

dx

d

(2x+1)

3

=

16

9

π×3(2x+1)

2

×2=

8

27

π(2x+1)

2

.