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kodGreya [7K]
3 years ago
7

A cone has a radius of 4 units and a height of 6 units. Its volume is (A. 96 / B. 100.48 / C. 301.44 / D. 401.92) cubic units. I

f a cylinder has the same radius and the same height as the cone, then its volume is (A. 66.99 / B. 288 C. / 301.44 / D. 904.32) cubic units.
Mathematics
1 answer:
Fed [463]3 years ago
8 0

Answer:

<h2>A cone: B. V = 100.48 cubic units</h2><h2>A cylinder: C. V = 301.44 cubic units</h2>

Step-by-step explanation:

The formula of a volume of a cone:

V=\dfrac{1}{3}\pi r^2H

<em>r</em> - radius

<em>H</em> - height

We have <em>r = 4 u</em> and <em>H = 6 u</em>. Substitute:

V=\dfrac{1}{3}\pi(4^2)(6)=\dfrac{1}{3}\pi(16)(6)=\dfrac{1}{3}\pi(96)=32\pi\ u^3

\pi\approx3.14\to V\approx(32)(3.14)=100.48\ u^3

If the cylinder has the same radius and height as a cone, then the volume of the cylinder is three times larger than the volume of the cone.

Therefore, the volume of acylinder:

V\approx3(100.48)=301.44\ u^3

Why?

The formula of a volume of a cone:

V_{cone}=\dfrac{1}{3}\pi r^2H

The formula of a volume of a cylinder:

V_{cylinder}=\pi r^2H

Therefore

V_{cone}=\dfrac{1}{3}V_{cylinder}\to V_{cylinder}=3V_{cone}

If the radius and height are the same.

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