Question

If the volume of the cylinder is 112π cubic feet and
the circumference of the circular base is 8π feet,
what is the height of the cylinder, in feet?

Answer 1

$\bf \large{ Given : }$

• Volume of cylinder = 112π

• Circumference of Base = 8π

$\bf \large{ To \: Find : }$

• Height of the Cylinder

$\bf \large{ Solution : }$

We know that A Cylinder has two circular plane ends. Two plane ends are parallel and are known as bases of the Cylinder.

Let's Find the radius from the given Circumference

$\bigstar \boxed{ \red{ \sf \: Circumference \: of \: circle = 2\pi \: r}}$

$\longrightarrow \sf \: 8 \cancel\pi = 2 \cancel\pi \: r$

$\longrightarrow \sf \: 2r = 8$

$\longrightarrow \sf \:r = \cancel\dfrac{8}{2}$

$\longrightarrow \sf \:r = 4 \: feet$

Now,

$\bigstar \boxed{ \red{ \sf \: Volume \: of \: Cylinder = \pi {r}^{2} h}}$

$\longrightarrow \sf112 \cancel\pi = \cancel\pi( {4}^{2} )h$

$\longrightarrow \sf \: 112 = 16h$

$\longrightarrow \sf \: h = \cancel\dfrac{112}{16}$

$\longrightarrow \sf \: h = 7 \: feet$

Hence,Height of the Cylinder is 7 Feet

Answer 2

AnSwEr :-

Height of Cylinder (h) = 7 ft

GiVeN :-

• Volume of the cylinder = 112π cubic feet

• Circumference of circular base = 8π feet

To FiNd :-

• Height (h) of the cylinder

SoLuTiOn :-

We know that,

• Circumference of Circle = 2πr

Hence,

The base of cylinder is circular in shape

And

• Circumference of Circular Base = 8π feets. --- ( given)

So,

$\implies2\pi \times r = 8\pi \\ \implies r = \frac{8\pi}{2\pi} \\ \implies \: r = 4ft$

Now,

We know that volume of cylinder is

$\implies \pi \: \times {r}^{2} h$

And

• Volume of Cylinder = 112π cubic feet. --- ( given)

So,

$\implies \: \pi \times {4}^{2} \times h = 112\pi \\ \implies \: h = \frac{112\pi}{16\pi} \\ \implies \: h = 7 \: ft$

Hence,

Height (h) = 7 feet