Question:
If the height and radius of a right circular cylinder are equal and its volume is $\dfrac{176}{7}\,\text{cm}^3$, find the diameter of the cylinder.
If the height and radius of a right circular cylinder are equal and its volume is $\dfrac{176}{7}\,\text{cm}^3$, find the diameter of the cylinder.
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When height and radius of a cylinder are equal, the volume formula simplifies to \(V = \pi r^3\), which makes calculations faster.
Updated On: Jan 25, 2026
- 4 cm
- 8 cm
- 2 cm
- 5 cm
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The Correct Option is A
Solution and Explanation
Step 1: Write the formula for volume of a right circular cylinder.
The volume \(V\) of a cylinder is given by:
\[ V = \pi r^2 h \]
Step 2: Use the given condition that height equals radius.
It is given that:
\[ h = r \]
Substitute \(h = r\) into the volume formula.
Step 3: Substitute known values into the formula.
\[ \pi r^2 r = \frac{176}{7} \]
\[ \pi r^3 = \frac{176}{7} \]
Step 4: Substitute the value of $\pi$.
Taking \( \pi = \frac{22}{7} \), we get:
\[ \frac{22}{7} r^3 = \frac{176}{7} \]
Step 5: Simplify the equation.
Multiply both sides by 7 to cancel the denominator.
\[ 22 r^3 = 176 \]
\[ r^3 = 8 \]
Step 6: Find the value of the radius.
\[ r = \sqrt[3]{8} = 2 \text{ cm} \]
Step 7: Find the diameter of the cylinder.
The diameter is given by:
\[ d = 2r \]
\[ d = 2 \times 2 = 4 \text{ cm} \]
Step 8: Final conclusion.
Hence, the diameter of the cylinder is 4 cm.
The volume \(V\) of a cylinder is given by:
\[ V = \pi r^2 h \]
Step 2: Use the given condition that height equals radius.
It is given that:
\[ h = r \]
Substitute \(h = r\) into the volume formula.
Step 3: Substitute known values into the formula.
\[ \pi r^2 r = \frac{176}{7} \]
\[ \pi r^3 = \frac{176}{7} \]
Step 4: Substitute the value of $\pi$.
Taking \( \pi = \frac{22}{7} \), we get:
\[ \frac{22}{7} r^3 = \frac{176}{7} \]
Step 5: Simplify the equation.
Multiply both sides by 7 to cancel the denominator.
\[ 22 r^3 = 176 \]
\[ r^3 = 8 \]
Step 6: Find the value of the radius.
\[ r = \sqrt[3]{8} = 2 \text{ cm} \]
Step 7: Find the diameter of the cylinder.
The diameter is given by:
\[ d = 2r \]
\[ d = 2 \times 2 = 4 \text{ cm} \]
Step 8: Final conclusion.
Hence, the diameter of the cylinder is 4 cm.
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