Banking Quantitative Aptitude Sample Paper Quantitative Aptitude Sample Paper-1

A cylinder whose height is \[\frac{2}{3}\]of its diameter has same volume as that of a sphere of radius 8 cm. The radius of base of the cylinder is

A) 8 cm

B) 4 cm

C) 2 cm

D) 5 cm

Correct Answer: A

Solution :

[a] Height of the cylinder\[=\frac{2}{3}\times \][Diameter of sphere

Height \[=\,\,\frac{4\times Radius}{3}\] [\[\because \]Diameter\[=2\times \]Radius]

Volume of sphere \[=\frac{4}{3}\pi \times {{(8)}^{3}}\]

Now, volume of cylinder \[=\pi {{r}^{2}}\times h=\pi \times {{r}^{2}}\times \frac{4r}{3}\]

\[\Rightarrow \] \[\frac{4}{3}\times \pi \times {{(8)}^{3}}=\pi \times {{r}^{2}}\times \frac{4r}{3}\]

\[\Rightarrow \] \[4\times 512=4{{r}^{3}}\]\[\Rightarrow \]\[r=8\,cm\]

Alternate Method

Height of the cylinder \[=\frac{4}{3}\times Radius\]

Hence, radius of the sphere and cylinder are same i.e. 8 cm.