A cube of gold with an edge length of 3 inches (in) is melted and reformed into a rectangular prism with a width of 2.5 in and a height of 2in. If the volume is unchanged during melting, what is the length of the prism of gold in inches?

Calculate volume of original gold cube: Calculate the volume of the original gold cube using the formula for the volume of a cube, V = s^3, where s is the side length of the cube. Given side length (s) = 3 inches. V = 3^3 = 27 cubic inches.Determine volume of rectangular prism: Determine the volume of the rectangular prism using the formula for the volume of a rectangular prism, V = lwh, where l is the length, w is the width, and h is the height. Since the volume is unchanged during melting, the volume of the rectangular prism is also 27 cubic inches. Given width (w) = 2.5 inches and height (h) = 2 inches.Solve for length of rectangular prism: Solve for the length (l) of the rectangular prism using the volume equation, V = lwh. 27 = l * 2.5 * 2 l = 27 / (2.5 * 2)Calculate length of rectangular prism: Calculate the length (l) of the rectangular prism. l = 27 / 5 l = 5.4 inches.

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A cube of gold with an edge length of 3 inches (in) is melted and reformed into a rectangular prism with a width of 2.5 in and a height of
2in. If the volume is unchanged during melting, what is the length of the prism of gold in inches?

A cube of gold with an edge length of $3$ inches (in) is melted and reformed into a rectangular prism with a width of $2$ . $5$ in and a height of $2 \mathrm{in}$ . If the volume is unchanged during melting, what is the length of the prism of gold in inches?

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Q. A cube of gold with an edge length of

3

inches (in) is melted and reformed into a rectangular prism with a width of

2

5

in and a height of

2 \mathrm{in}

. If the volume is unchanged during melting, what is the length of the prism of gold in inches?

Calculate volume of original gold cube: Calculate the volume of the original gold cube using the formula for the volume of a cube, $V = s^3$ , where $s$ is the side length of the cube. $\newline$ Given side length ( $s$ ) = $3$ inches. $\newline$ $V = 3^3 = 27$ cubic inches.
Determine volume of rectangular prism: Determine the volume of the rectangular prism using the formula for the volume of a rectangular prism, $V = lwh$ , where $l$ is the length, $w$ is the width, and $h$ is the height. $\newline$ Since the volume is unchanged during melting, the volume of the rectangular prism is also $27$ cubic inches. $\newline$ Given width ( $w$ ) = $2.5$ inches and height ( $h$ ) = $2$ inches.
Solve for length of rectangular prism: Solve for the length $l$ of the rectangular prism using the volume equation, $V = lwh$ . $27 = l \times 2.5 \times 2$ $l = \frac{27}{2.5 \times 2}$
Calculate length of rectangular prism: Calculate the length $l$ of the rectangular prism. $l = \frac{27}{5}$ $l = 5.4 \text{ inches}.$