Question

The volume of rectangular solid is 810 cm^3. Find it's dimension of they are in the ratio of 2:3:5.

Answer 1

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Answer on Question #81348 – Math – Geometry

Question

The volume of rectangular solid is $810~\mathrm{cm}^3$. Find it's dimension of they are in the ratio of 2:3:5.

Solution

Let sides of the rectangular solid be $2x, 3x, 5x$. It arises from the ratio 2:3:5. Now, the volume $V$ will be

$$V = 2x \cdot 3x \cdot 5x = 30x^3 = 810.$$

From this equation we can find $x$ which needed for getting dimensions of the solid.

$$x^3 = 27,$$ $$x = 3.$$

Then $2x = 2 \cdot 3 = 6~\mathrm{cm}$, $3x = 3 \cdot 3 = 9~\mathrm{cm}$, $5x = 5 \cdot 3 = 15~\mathrm{cm}$.

**Answer**: dimensions of rectangular solid are 6 cm, 9 cm and 15 cm.

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