Question

A solid is in the shape of a conestanding on a hemisphere with both their radii being equal to $12$ m and height of the cone is $5$ m. Find the volume of the solid. (Use $\pi =3$)

• A. $1392\pi m^3$
• B. $4176\pi m^3$
• C. $1028\pi m^3$
• D. $1308\pi m^3$

Answer 1

Answer: (A)

$1392\pi m^3$

The question asked is wrong. It should be A solid is in the shape of a cone standing on a hemisphere. Because if a bowl, which is also a hemisphere, mounted on another hemisphere then it becomes a sphere. In which the height of sphere is equal to its diameter. So, there should cone mounted on hemisphere.

Volume of solid $=$ volume of cone + volume of hemisphere

$=$ $\frac{1}{3}\pi r^{2}h+\frac{2}{3}\pi r^3$

$=$ $\frac{1}{3}\pi r^2(h+2r)$

$=$ $\frac{1}{3}\times 3\times 12\times 12(5+2\times 12)=144\times (5+24)$

$=$ $144\times 29=4176m^3$