question_answer

From a right circular cylinder of radius\[\text{1}0\text{cm}\times \]height 21 cm a right circular cone of same base radius is removed. If the volume of the remaining portion is 4,400 cm3, then the height of the cone removed is

A)  15 cm             

B)         18 cm

C)  21 cm                

D)         24 cm

Correct Answer: C

Solution :

 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 \[=\frac{1}{3}\pi {{(10)}^{2}}h=\frac{100}{3}\pi h\,\,c{{m}^{3}}\] By hypothesis,                 \[2100\pi -\frac{100}{3}\,\pi \,\,h=4,400\] or            \[(6300-100h)\,\pi =13,200\] or            \[6,300-100\,h=\frac{13,200\times 7}{22}=4,200\] or            \[100\,h=6,300-4,200=2,100\] or            \[h=21\,cm\]