Question

Height of a solid cylinder is $10$ cm and diameter $8$ cm. Two equal conical holes have been made from both the ends of cylinder. If the diameter of the hole is $6$ m and height $4$ cm. The volume of the remaining portion is

• A. $24\pi {\text{cm}}^3$
• B. $36\pi {\text{cm}}^3$
• C. $72\pi {\text{cm}}^3$
• D. $136\pi {\text{cm}}^3$

Answer 1

Answer: (D)

$136\pi {\text{cm}}^3$

Dimensions of Cylinder:

Height $h=10cm$

Radius, $r=4$

Dimensions of Cones:

Height, $H=4cm$

Radius, $R=3cm$

The volume of Cylinder $=\pi r^{2}h$

The volume of two Cones $=2\pi R^{2}H/3$

Remaining volume= Volume of Cylinder-Volume of two Cones

$V=\pi r^{2}h-2\pi R^{2}H/3$

$V=\pi 16\ast 10-2\pi 9\ast 4/3$

$V=160\pi -24\pi$

$V=136\pi c{m}^3$