The radius of a sphere is increasing at a rate of 3 mm/s. how fast is the volume of the sphere increasing when the diameter is 10 mm?

We will find the rate of change of volume with respect to the change of radius.

Volume, V(r) = (4/3) π r^3

Find rate of change of volume with respect to change of radius by differentiation

V'(r)=dV/dr = d[(4/3) π r^3]/dr = (4/3) π d[r^3]/dr =(4/3) π 3r^2

Therefore when diameter=10mm, r=5mm

V'(r)=V'(5)=(4/3) π (3(5^2))=(4/3) π 75 = 100 π mm^3/mm

the dimensions are:

step-by-step explanation:

we want to find the dimensions of a rectangular box with volume of

we factor to obtain;

we rewrite the rightmost factor to obtain;

recall that:

we apply difference of two squares formula to obtain;

hence the dimensions are

distance covered by pamela in 9 l of fuel = 99km

let us apply unitary method here.

distance covered by pamela in 1 l of fuel =99/9 =11 km

now let us find distance covered by pamela if she has 12 l of fuel.

distance covered in 12 l = distance covered in 1 l of fuel * 12

we know that distance covered by here in 1 l is 11 km.

so distance covered in 12 l of fuel = 11*12 = 132 km.