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ASAP!! ITS URGENT

Find the slant height of a cone if the volume is 301.44 mm^3 and the altitude is 8 mm.

User Amit Anand
by
7.5k points

1 Answer

1 vote
The formula for the volume of a cone is:

V = (1/3)πr^2h

Where V is the volume, r is the radius of the base, h is the altitude (height) of the cone, and π is approximately 3.14159.

We can rearrange this formula to solve for the radius:

r = sqrt((3V)/(πh))

Plugging in the given values, we get:

r = sqrt((3 x 301.44)/(π x 8)) = 6 mm

Now, we can use the Pythagorean theorem to find the slant height of the cone:

l = sqrt(r^2 + h^2)

Plugging in the values we have, we get:

l = sqrt(6^2 + 8^2) = sqrt(100) = 10 mm

Therefore, the slant height of the cone is 10 mm.
User Sarah West
by
8.4k points
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