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

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

The volume of the unfilled volume is   cubic units

Step-by-step explanation:

Step 1: Find the volume of a cylinder

we know that

volume of a cylinder  =

Where

r is the radius of the cylinder

h is the height of the cylinder

On Substituting the values

volume of a cylinder  =

volume of a cylinder  =

volume of a cylinder   =   cubic units

Step 2: Find the volume of a cone

volume of a cone is =

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 = 15 units

Now the volume is

=

=>

=>

=> 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   =   =   cubic units

10 * 563.67 = 5636.7

expression #3 is not equivalent. the others are.