Question

What is the unfilled volume inside the cylinder?

Answer 1

Question:

A solid oblique cone with a slant length of 17 units is placed inside an empty cylinder with a congruent base of radius 8 units and a height of 15 units. What is the unfilled volume inside the cylinder? 320π cubic units 597π cubic units 640π cubic units 725π cubic units

Answer:

The volume of the unfilled volume is  $640 \pi$ cubic units

Step-by-step explanation:

Step 1: Find the volume of a cylinder

we know that

volume of a cylinder  = $\pi r^2 h$

Where

r is the radius of the cylinder

h is the height of the cylinder

On Substituting the values

volume of a cylinder  = $\pi (8) ^2 (15)$

volume of a cylinder  = $\pi (64) (15)$

volume of a cylinder   =  $960 \pi$ cubic units

Step 2: Find the volume of a cone

volume of a cone is = $\frac{1}{3} \pi r^2 h$

r is the radius

h is the height

we have given with slant height L =  17 units

Applying the Pythagorean Theorem find the value of h

$h^2 = l^2 - r^2$

$h^2 = (17)^2 - (8)^2$

$h^2 = 289 - 64$

$h^2 = 225$

h = 15 units

Now the volume is

= $\frac{1}{3} \pi(8)^2 15$

=>$\frac{1}{3} \pi (64) 15$

=> $\frac{960}{3} \pi$

=>$320 \pi$ cubic units

Step  3  :Finding  the unfilled volume inside the cylinder

Unfilled volume inside the cylinder   =  volume of the cylinder - volume of the cone

Unfilled volume inside the cylinder   =   $960\pi - 320\pi$ =  $640 \pi$ cubic units