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.

• A. 4 cm
• B. 8 cm
• C. 2 cm
• D. 5 cm

Hint:

When height and radius of a cylinder are equal, the volume formula simplifies to \(V = \pi r^3\), which makes calculations faster.

Answer 1

The Correct Option is A

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.