Question
In a right prism with a square base, volume = $1024 \text{ cm}^3$ and height = 16 cm. What is the side of the square base?
This question was previously asked in
SSC CGL 2025 Tier 1 Question Paper (25-Sep-2025) (Shift 3)
The correct answer is
8 cm
Prism Volume Calculation
The volume ($V$) of a right prism is calculated using the formula:
$ V = \text{Area of Base} \times \text{Height} $For a prism with a square base of side length $s$, the area of the base is $s^2$. Therefore, the volume formula becomes:
$ V = s^2 \times h $Where $V$ is the volume and $h$ is the height.
Finding the Square Base Side
We are given:
- Volume ($V$) = $1024 \text{ cm}^3$
- Height ($h$) = $16 \text{ cm}$
We need to find the side length ($s$) of the square base.
Calculating the Side Length
Substitute the given values into the volume formula:
$ 1024 \text{ cm}^3 = s^2 \times 16 \text{ cm} $To find $s^2$, rearrange the equation:
$ s^2 = \frac{1024 \text{ cm}^3}{16 \text{ cm}} $ $ s^2 = 64 \text{ cm}^2 $Now, find the side length $s$ by taking the square root:
$ s = \sqrt{64 \text{ cm}^2} $ $ s = 8 \text{ cm} $The side length of the square base is 8 cm.
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