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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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Convert between customary and metric systems

Full solution

Q. 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 Formula: Identify the formula for the volume of a right circular cylinder. $\newline$ The volume $V$ of a right circular cylinder is given by the formula $V = \pi r^2 h$ , where $r$ is the radius and $h$ is the height of the cylinder.
Plug in Values: Plug in the given values for the radius and height into the volume formula. $\newline$ Given: radius $r = 4$ feet, height $h = 30$ feet $\newline$ Volume $V = \pi \times (4 \text{ feet})^2 \times 30 \text{ feet}$
Calculate Volume: Calculate the volume using the given values. $\newline$ Volume $V = \pi \times 16 \text{ feet}^2 \times 30 \text{ feet}$ $\newline$ Volume $V = \pi \times 480 \text{ feet}^3$
Identify Value of a: Identify the value of a from the expression for the volume. $\newline$ The volume is given as $a \pi$ cubic feet, which means $V = a \cdot \pi \, \text{feet}^3$ . $\newline$ From our calculation, we have $V = \pi \cdot 480 \, \text{feet}^3$ . $\newline$ Therefore, $a = 480$ .

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