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Find the volume of the solid generated when the rectangle below is rotated about side
bar(SV). Round your answer to the nearest tenth if necessary.

$1$ . Find the volume of the solid generated when the rectangle below is rotated about side $\overline{S V}$ . Round your answer to the nearest tenth if necessary.

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Find the rate of change of one variable when rate of change of other variable is given

Full solution

Q.

1

. Find the volume of the solid generated when the rectangle below is rotated about side

\overline{S V}

. Round your answer to the nearest tenth if necessary.

Identify dimensions and axis: Identify the dimensions of the rectangle and the axis of rotation. Assume the rectangle has length $l$ and width $w$ , and it is rotated about the side of length $l$ .
Form cylinder solid: The solid formed is a cylinder with height $l$ and radius $w$ . The volume of a cylinder is $V = \pi r^2 h$ , where $r$ is the radius and $h$ is the height.
Substitute values into formula: Substitute the known values into the volume formula. If the rectangle's width is ' extit{w}' and length is ' extit{l}', then the volume $V = \pi w^2 l$ .
Calculate volume: Calculate the volume using the given dimensions. Since the problem doesn't provide specific numbers, we can't calculate the exact volume. We need the actual measurements of $w$ and $l$ to proceed.
Need actual measurements: Without the measurements, we cannot find the volume. We need the actual values for $w$ and $l$ to complete the calculation.

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