The surface area of a cube is 1734 sq. cm. Find its volume.Choices:- 2334 cubic.cm 3356 cubic.cm 4913 cubic.cm 3478 cubic.cm

1. Break Down the Problem

To find the volume of a cube given its surface area, we can use the relationship between the surface area and the volume of a cube.

2. Relevant Concepts

• The formula for the surface area $A$ of a cube is given by: $A = 6s^2$ where $s$ is the length of a side of the cube.

• The formula for the volume $V$ of a cube is given by: $V = s^3$

3. Analysis and Detail

Given the surface area: $A = 1734 \text{ sq. cm}$ we can rearrange the surface area formula to solve for $s$: $s^2 = \frac{A}{6}$ Substituting the value of $A$: $s^2 = \frac{1734}{6} = 289$ Taking the square root to find $s$: $s = \sqrt{289} = 17 \text{ cm}$

Now, using the side length $s$ to find the volume: $V = s^3 = 17^3$ Calculating $17^3$: $17^3 = 17 \times 17 \times 17 = 289 \times 17 = 4913 \text{ cubic cm}$

4. Verify and Summarize

We calculated the side length to be 17 cm, and the subsequent volume is confirmed as $4913$ cubic cm.

Final Answer

The volume of the cube is $\mathbf{4913} \text{ cubic cm}$.