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

Question

1 month ago

10

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

2 answers:

PIT_PIT [12.4K] · Answer 1 · 2026-02-25T12:47:21+03:00

Step $1$

Calculate the volume of a cylinder

We understand that

the volume of a cylinder can be expressed as

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

In this scenario

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

Insert the values

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

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

Step $2$

Calculate the volume of a cone

We are aware that

the volume of a cone equals

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

In this example

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

Use the Pythagorean Theorem to determine the height 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 $3$

Calculate the empty volume inside the cylinder

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

Thus

the final result is

the empty volume inside the cylinder is $640\pi \ units^{3}$

zzz [12.3K] · Answer 2 · 2026-02-25T12:50:29+03:00

4 0

Answer:

The correct result is 640

Step-by-step clarification:

I solved it online