Question

From a right circular cylinder of radius $10$ cm $\times$ height $21$ cm a right circular cone of same base radius is removed. If the volume of the remaining portion is $4,400$ $c{m}^3$, then the height of the cone removed is

• A. $15$ cm
• B. $18$ cm
• C. $21$ cm
• D. $24$ cm

Answer 1

The correct option is C $21$ cm

Volume of, cylinder $=\pi (10{)}^{2}21=2$, $100\pi c{m}^3$
If $h$ be the height of the cone, then
Volume of cone $=\frac{1}{3}\pi (10{)}^{2}h=\frac{100}{3}\pi hc{m}^3$
By hypothesis,
$2100\pi -\frac{100}{3}\pi h=4,400$
$\Rightarrow (6300-100h)\pi =13,200$
$\Rightarrow 6,300-100h=\frac{13,200\times 7}{22}=4,200$
$\Rightarrow 100h=6,300-4,200=2,100$
$\Rightarrow h=21$ cm