Question

Calculate the radius (in inches) of the base of a cylindrical container of volume $440{\text{in}}^3$. Height of the cylindrical container is 35 inches. $(\text{Take}\pi =\frac{22}{7})$

• A. $3$
• B. $5$
• C. $2$
• D. $4$

Answer 1

The correct option is C $2$

Height of the cylindrical container $=h=35\text{inches}$
Let the radius of the cylindrical container be $“r”$.
We know that the volume of the cylindrical container is given by the formula:
Volume of the cylinder $=\pi r^{2}h$
Volume of the cylindrical container $=440{\text{in}}^3$
$\Rightarrow \pi r^{2}h=440$ (equating with the formula for volume)
$\Rightarrow \frac{22}{7}\times r^2\times 35=440$ (substituting for h and $\pi$)
$\Rightarrow r^2=\frac{440\times 7}{22\times 35}$ (transposing $\frac{22}{7}$ and 35 to R.H.S.)
$\Rightarrow r^2=4$ (simplifying)
$\Rightarrow r=\sqrt{4}$ (taking square root of each side)
$\Rightarrow r=2\text{inches}$
Therefore, the radius of the base of a cylindrical container is 2 inches.
$\to$Option A is correct.