Question

The volume of this right circular cylinder is 64π cubic yards. If h, the height of the cylinder, is 4 yards, what is r, the radius of the base?

Answer 1

h = 4 cm

Explanation:

The formula for volume of a cylinder is

V = πr²h where V is the volume, r is the radius, and h is the height.

We are given V = 64π, and r = 4, plug those in and solve for h

64π = π(4²)h

64π = 16πh

(64π)/(16π) = (16πh)/(16π) (divide both sides by 16π)

4 = (16π)/(16π)h

4 = h

Answer 2

• Radius = 4 yards

Solution:

Here, we are provided a right circular cylinder with :

• Volume = 64 π cubic yards
• Height = 4 yards
• Radius = ?

We know that :

`\quad\hookrightarrow\quad{\pmb{ \mathfrak { Volume = \pi r^2 h }}}`

Therefore,

`\implies\quad \sf{V = \pi r^2 h }`

`\implies\quad \sf{64\pi = \pi r^2 * 4 }`

`\implies\quad \sf{ \pi r^2 * 4 = 64\pi}`

`\implies\quad \sf{r^2 =(64\pi)/(\pi * 4) }`

`\implies\quad \sf{ r^2 =\frac{\cancel{64}}{\cancel{4}}* \cancel{(\pi)/(\pi)}}`

`\implies\quad \sf{ r^2 = 16}`

`\implies\quad \sf{r=√(16) }`

`\implies\quad \underline{\underline{\pmb{\sf{r= 4}}} }`