Question

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. If 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.

Answer 1

Answer:

A cone: B. V = 100.48 cubic units

A cylinder: C. V = 301.44 cubic units

Step-by-step explanation:

The formula of a volume of a cone:

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

r - radius

H - height

We have r = 4 u and H = 6 u. 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.