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The volume of a cylinder is 30 pie cubic units. A cone shares the same base. The height of the cone is twice the height of the c

bija089 [108]

<u>Given</u>:

The volume of a cylinder is $30 \pi$ cubic units.

A cone shares the same base.

The height of the cone is twice the height of the cylinder.

We need to determine the volume of the cone.

<u>Height of the Cone:</u>

Let h denote the height of the cylinder.

Let H denote the height of the cone.

Since, it is given that, the height of the cone is twice the height of the cylinder, we have;

$H=2h$

<u>Volume of the cylinder:</u>

The formula to determine the volume of the cylinder is

$V=\pi r^2 h$

Since, volume of the cylinder is $30 \pi$ , we get;

$30 \pi = \pi r^2 h$ -------(1)

<u>Volume of the cone:</u>

The formula to determine the volume of the cone is

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

Substituting $H=2h$ , we get;

$V=\frac{1}{3} \pi r^2 (2h)$

$V=\frac{2}{3} \pi r^2 h$

Substituting equation (1), we get;

$V=\frac{2}{3} (30 \pi)$

$V=20 \pi$

Thus, the volume of the cone is 20π

Hence, Option C is the correct answer.

4 0

3 years ago

(01.02 LC)Simplify negative 3 and 1 over 9 − negative 8 and 1 over 3.

blsea [12.9K]

As we are given with

$-3\frac{1}{9}-(-8\frac{1}{3})\\\\$

we are supposed to simplify this expression. which can be done as below

$\\=-3\frac{1}{9}+8\frac{1}{3}\\\\=\frac{-28}{9}+\frac{25}{3}\\\\=\frac{-28+75}{9}\\\\=-\frac{47}{9}\\$

$=5\frac{2}{9}$

6 0

3 years ago

A graph titled velocity versus time has horizontal axis time (seconds) and vertical axis velocity (meters per second). A line ha

AnnyKZ [126]

Acceleration is the change in velocity with respect to the time. The acceleration of the car at segment C is -30 meter per second squared. Hence the option B is the correct option.

<h3>Given information-</h3>

Segment A runs from 0 seconds 0 meters per second to 1 seconds 30 meters per second.

Segment B runs to 3 seconds 30 meters per second.

Segment C runs to 6 seconds 10 meters per second.

Segment D runs to 7 seconds 10 meters per second.

Segment E runs to 10 seconds 20 meters per second.

<h3>Acceleration</h3>

Acceleration is the change in velocity with respect to the time. Acceleration of a vector quantity which means it has both magnitude and the direction. It can be given as,

$a=\dfrac{\Delta v}{\Delta t}$