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
