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V=pir^(2)h
The formula gives the volume
V of a right circular cylinder with radius
r and height
h. If the volume of a right circular cylinder with a radius of 4 feet and a height of 30 feet is
a pi cubic feet, what is the value of
a ?

$V=\pi r^{2} h$ $\newline$ The formula gives the volume $V$ of a right circular cylinder with radius $r$ and height $h$ . If the volume of a right circular cylinder with a radius of $4$ feet and a height of $30$ feet is $a \pi$ cubic feet, what is the value of $a$ ?

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Find trigonometric ratios using a Pythagorean or reciprocal identity

Full solution

Q.

V=\pi r^{2} h

\newline

The formula gives the volume

V

of a right circular cylinder with radius

r

and height

h

. If the volume of a right circular cylinder with a radius of

4

feet and a height of

30

feet is

a \pi

cubic feet, what is the value of

a

?

Identify given values and formula: Identify the given values and the formula to use. $\newline$ We are given the radius $r = 4$ feet and the height $h = 30$ feet. The volume $V$ of a right circular cylinder is given by the formula $V = \pi r^2 h$ .
Substitute given values into formula: Substitute the given values into the formula. $\newline$ Using the given radius and height, we substitute into the formula: $\newline$ $V = \pi \times (4 \text{ feet})^2 \times (30 \text{ feet})$
Calculate the volume: Calculate the volume $V$ . $\newline$ First, square the radius: $\newline$ $(4 \text{ feet})^2 = 16 \text{ feet}^2$ $\newline$ Then, multiply by the height and $\pi$ : $\newline$ $V = \pi \times 16 \text{ feet}^2 \times 30 \text{ feet}$ $\newline$ $V = \pi \times 480 \text{ feet}^3$
Identify value of 'a' in expression: Identify the value of $a$ in the expression $V = a imes ext{π} ext{ cubic feet}$ . $\newline$ From the previous step, we have $V = ext{π} imes$ $480$ ext{ feet}^ $3$ . This means that $a$ is the coefficient of $ext{π}$ in the volume expression, which is $480$ .

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