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

A cone has a radius of 4 units and a height of 6 units.

Its volume is

[100.48]

cubic units. If a cylinder has the same radius and the same height as the cone, then its volume is

[301.44]

cubic units.

Explanation:

Answer 2

A cone: B. V = 100.48 cubic units

A cylinder: C. V = 301.44 cubic units

Explanation:

The formula of a volume of a cone:

`V=(1)/(3)\pi r^2H`

r - radius

H - height

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

`V=(1)/(3)\pi(4^2)(6)=(1)/(3)\pi(16)(6)=(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)=(1)/(3)\pi r^2H`

The formula of a volume of a cylinder:

`V_(cylinder)=\pi r^2H`

Therefore

`V_(cone)=(1)/(3)V_(cylinder)\to V_(cylinder)=3V_(cone)`

If the radius and height are the same.