Question

What is the unfilled volume inside the cylinder?

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.

3202 cubic units
5971 cubic units
6407 cubic units
7252 cubic units

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

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 =
`(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

=
`(1)/(3) \pi(8)^2 15`

=>
`(1)/(3) \pi (64) 15`

=>
`(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