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

Respuesta :

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  [tex]640 \pi[/tex] cubic units

Step-by-step explanation:

Step 1: Find the volume of a cylinder

we know that

volume of a cylinder  = [tex]\pi r^2 h[/tex]

Where

r is the radius of the cylinder

h is the height of the cylinder

On Substituting the values

volume of a cylinder  = [tex]\pi (8) ^2 (15)[/tex]

volume of a cylinder  = [tex]\pi (64) (15)[/tex]

volume of a cylinder   =  [tex]960 \pi[/tex] cubic units

Step 2: Find the volume of a cone

volume of a cone is = [tex]\frac{1}{3} \pi r^2 h[/tex]

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

[tex]h^2 = l^2 - r^2[/tex]

[tex]h^2 = (17)^2 - (8)^2[/tex]

[tex]h^2 = 289 - 64[/tex]

[tex]h^2 = 225[/tex]

h = 15 units

Now the volume is

= [tex]\frac{1}{3} \pi(8)^2 15[/tex]

=>[tex]\frac{1}{3} \pi (64) 15[/tex]

=> [tex]\frac{960}{3} \pi[/tex]

=>[tex]320 \pi[/tex] 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   =   [tex]960\pi - 320\pi[/tex] =  [tex]640 \pi[/tex] cubic units

Answer:640 pi

Step-by-step explanation:edge 2020

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