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 1

Step $1$

Find the volume of a cylinder

we know that

volume of a cylinder is equal to

$V1=\pi r^{2} h$

in this problem

$r=8\ units \\ h=15\ units$

Substitute

$V1=\pi 8^{2} 15$

$V1=960\pi\ units^{3}$

Step $2$

Find the volume of a cone

we know that

volume of a cone is equal to

$V2=\frac{1}{3}\pi r^{2} h$

in this problem

$r=8\ units \\ l=17\ units \\ h=?$

applying the Pythagorean Theorem find the value of h

$h^{2} =l^{2}-r^{2}\\ h^{2} =17^{2}-8^{2}\\ h^{2}=225\\ h=15\ units$

$V2=\frac{1}{3}\pi 8^{2} 15\\ \\ V2=320\pi \ units^{3}$

Step $3$

Find the unfilled volume inside the cylinder

$V1-V2=960\pi -320\pi =640\pi \ units^{3}$

therefore

the answer is

the unfilled volume inside the cylinder is equal to $640\pi \ units^{3}$

Answer 2

Answer:

Correct answer is 640

Step-by-step explanation:

Did it online