Respuesta :
Answer:
*The height is 6 units.
*The radius is 8 units.
*The volume is exactly [tex]128\pi[/tex] cubic units.
An approximation for the volume would be [tex]402.124[/tex] cubic units.
Step-by-step explanation:
To find the radius, we will have to use Pythagorean Theorem (or remember some Pythagorean Triples-either way).
Slant height=10 units (this is the hypotenuse length)
Radius=r units (trying to find this leg length)
Height=6 units (we are given this leg length)
So we have to solve:
[tex]r^2+6^2=10^2[/tex]
[tex]r^2+36=100[/tex]
Subtract 36 on both sides:
[tex]r^2=64[/tex]
Square root both sides:
[tex]r=\sqrt{64}=8[/tex]
The radius is 8 units.
To find the volume of a cone, we will use the formula [tex]V=\frac{1}{3} \pi r^2 h[/tex].
[tex]V=\frac{1}{3} \pi (8)^2 (6)[/tex]
[tex]V=\frac{1}{3} \pi (64) (6)[/tex]
[tex]V=\frac{1}{3}(64)(6) \pi[/tex]
[tex]V=128 \pi [/tex]
So the volume is exactly [tex]128\pi [/tex] units cubed.
An approximation for this volume would be 402.124 units cubed (if we took an approximation of pi and multiply it to 128).
The height is 6 units, the radius is 8 units, and the volume is 128π cubic units.
What is the volume of a cone?
Let r be the radius of the base circle and h be the height of the cone.
Then the volume of the cone will be
V = 1/3 x πr² x h
A cone has a height of 6 units and a slant length of 10 units.
Then the radius of the base circle will be
10² = 6² + r²
100 = 36 + r²
r² = 64
r = 8 units
Then the volume of the cone will be
V = 1/3 x π(8)² x 6
V = 128π cubic units
More about the volume of the cone link is given below.
https://brainly.com/question/1984638
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