Question

The value of the surface area of the cylinder is equal to the value of the volume of the cylinder. Find the value of x

Answer 1

Answer:

Height or x is 4.50 feet.

Step-by-step explanation:

Surface area is given as : $2\pi rh+2\pi r^{2}$

Volume is given as : $\pi r^{2} h$

The value of the surface area of the cylinder is equal to the value of the volume of the cylinder. This means:

$2\pi rh+2\pi r^{2}$ = $\pi r^{2} h$

Diameter is given as : $7\frac{1}{5} =\frac{36}{5} =7.2$ feet

So, radius = $7.2/2=3.6$ feet

height = h

SA = $2\times3.14\times3.6h+2\times3.14\times(3.6)^{2}$

= $22.61h+81.39$ feet square

Volume = $3.14\times(3.6)^{2} \times h$

= 40.70h cubic feet

Now as SA= volume ; we will equal both and solve for h;

$22.61h+81.39=40.70h$

=> $40.70h-22.61h=81.39$

=> $18.09h=81.39$

h = 4.50 feet

Hence, height or x is 4.50 feet.

So, SA = 183.12 square feet

Volume = 183.12 square feet

Answer 2

pi·(7.2/2)^2·x = 2·pi·(7.2/2)^2 + 2·pi·(7.2/2)·x

x = 4.5 = 4 1/2

O = V = 1458/25·pi = 58.32·pi