Math  /  Geometry

QuestionFind the volume VV of the described solid SS. a right circular cone with height 4h4 h and base radius 2r2 r

Studdy Solution

STEP 1

1. The solid is a right circular cone.
2. The height of the cone is 4h 4h .
3. The base radius of the cone is 2r 2r .

STEP 2

1. Recall the formula for the volume of a cone.
2. Substitute the given values for height and radius.
3. Calculate the volume.

STEP 3

Recall the formula for the volume of a cone:
V=13πr2h V = \frac{1}{3} \pi r^2 h

STEP 4

Substitute the given values for height and radius into the formula:
V=13π(2r)2(4h) V = \frac{1}{3} \pi (2r)^2 (4h)

STEP 5

Calculate the volume by simplifying the expression:
V=13π(4r2)(4h) V = \frac{1}{3} \pi (4r^2) (4h) =13π×16r2×4h = \frac{1}{3} \pi \times 16r^2 \times 4h =13×64πr2h = \frac{1}{3} \times 64 \pi r^2 h =643πr2h = \frac{64}{3} \pi r^2 h
The volume of the cone is:
643πr2h \boxed{\frac{64}{3} \pi r^2 h}

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