Question

The surface area of a cube is 1734 sq.cm. Find its volume.

• A. 5113 cm^3
• B. 4913 cm^3
• C. 5913 cm^3
• D. 6113 cm^3

Hint:

$a^2 = \frac{1734}{6} = 289 \implies a = 17\text{ cm} \implies V = 17^3 = 4913\text{ cm}^3$.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
For a cube of side length $a$, total surface area is $6a^2$ and volume is $a^3$.

Step 2: Key Formula or Approach:
Total surface area is given as $1734\,\text{cm}^2$:
\[6a^2 = 1734 \implies a^2 = \frac{1734}{6} = 289\] Taking square root:
\[a = \sqrt{289} = 17\,\text{cm}\]

Step 3: Detailed Explanation:
Volume of the cube:
\[V = a^3 = 17^3 = 17 \times 17 \times 17 = 4913\,\text{cm}^3\]

Step 4: Final Answer:
Therefore, the volume of the cube is 4913 cm^3.