QuestionFind the value of $a$ if the volume $V$ of a cylinder with radius 4 ft and height 30 ft is $a \pi$ cubic feet.

Studdy Solution

STEP 1

Assumptions1. The formula for the volume of a right circular cylinder is $V=\pi r^{} h$ . The radius $r$ of the cylinder is4 feet3. The height $h$ of the cylinder is30 feet4. The volume $V$ of the cylinder is given as $a \pi$ cubic feet5. We are asked to find the value of $a$

STEP 2

First, we need to substitute the given values of $r$ and $h$ into the formula for the volume of a right circular cylinder.
$V=\pi r^{2} h$

STEP 3

Now, plug in the given values for the radius $r$ and height $h$ to calculate the volume $V$ .
$V=\pi ()^{2} (30)$

STEP 4

Calculate the volume $V$ .
$V=\pi (4)^{2} (30) = \pi (16) (30) = \pi (480)$

STEP 5

Now that we have the volume $V$ of the cylinder, we can equate this to the given expression $a \pi$ to find the value of $a$ .
$a \pi = \pi (480)$

STEP 6

To find the value of $a$ , we can divide both sides of the equation by $\pi$ .
$a =480$ The value of $a$ is480.

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QuestionFind the value of $a$ if the volume $V$ of a cylinder with radius 4 ft and height 30 ft is $a \pi$ cubic feet.

Studdy Solution

STEP 1

Assumptions1. The formula for the volume of a right circular cylinder is $V=\pi r^{} h$ . The radius $r$ of the cylinder is4 feet3. The height $h$ of the cylinder is30 feet4. The volume $V$ of the cylinder is given as $a \pi$ cubic feet5. We are asked to find the value of $a$

STEP 2

First, we need to substitute the given values of $r$ and $h$ into the formula for the volume of a right circular cylinder.
$V=\pi r^{2} h$

STEP 3

Now, plug in the given values for the radius $r$ and height $h$ to calculate the volume $V$ .
$V=\pi ()^{2} (30)$

STEP 4

Calculate the volume $V$ .
$V=\pi (4)^{2} (30) = \pi (16) (30) = \pi (480)$

STEP 5

Now that we have the volume $V$ of the cylinder, we can equate this to the given expression $a \pi$ to find the value of $a$ .
$a \pi = \pi (480)$

STEP 6

To find the value of $a$ , we can divide both sides of the equation by $\pi$ .
$a =480$ The value of $a$ is480.

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QuestionFind the value of aaa if the volume VVV of a cylinder with radius 4 ft and height 30 ft is aπa \piaπ cubic feet.

Studdy Solution

STEP 1

Assumptions1. The formula for the volume of a right circular cylinder is V=πrhV=\pi r^{} hV=πrh . The radius rrr of the cylinder is4 feet3. The height hhh of the cylinder is30 feet4. The volume VVV of the cylinder is given as aπa \piaπ cubic feet5. We are asked to find the value of aaa

STEP 2

First, we need to substitute the given values of rrr and hhh into the formula for the volume of a right circular cylinder.V=πr2hV=\pi r^{2} hV=πr2h

STEP 3

Now, plug in the given values for the radius rrr and height hhh to calculate the volume VVV.V=π()2(30)V=\pi ()^{2} (30)V=π()2(30)

STEP 4

Calculate the volume VVV.V=π(4)2(30)=π(16)(30)=π(480)V=\pi (4)^{2} (30) = \pi (16) (30) = \pi (480)V=π(4)2(30)=π(16)(30)=π(480)

STEP 5

Now that we have the volume VVV of the cylinder, we can equate this to the given expression aπa \piaπ to find the value of aaa.aπ=π(480)a \pi = \pi (480)aπ=π(480)

STEP 6

To find the value of aaa, we can divide both sides of the equation by π\piπ.a=480a =480a=480The value of aaa is480.

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QuestionFind the value of $a$ if the volume $V$ of a cylinder with radius 4 ft and height 30 ft is $a \pi$ cubic feet.

Assumptions1. The formula for the volume of a right circular cylinder is $V=\pi r^{} h$ . The radius $r$ of the cylinder is4 feet3. The height $h$ of the cylinder is30 feet4. The volume $V$ of the cylinder is given as $a \pi$ cubic feet5. We are asked to find the value of $a$

First, we need to substitute the given values of $r$ and $h$ into the formula for the volume of a right circular cylinder.
$V=\pi r^{2} h$

Now, plug in the given values for the radius $r$ and height $h$ to calculate the volume $V$ .
$V=\pi ()^{2} (30)$

Calculate the volume $V$ .
$V=\pi (4)^{2} (30) = \pi (16) (30) = \pi (480)$

Now that we have the volume $V$ of the cylinder, we can equate this to the given expression $a \pi$ to find the value of $a$ .
$a \pi = \pi (480)$

To find the value of $a$ , we can divide both sides of the equation by $\pi$ .
$a =480$ The value of $a$ is480.