question_answer

A cylinder is surmounted by a cone at one end, a hemisphere at the other end. The common radius is 3.5 cm, the height of the cylinder is 6.5 cm and the total height of the structure is 12.8 cm. The volume V of the structure lies between

A) 370 and 380 cm

B) 380 and 390 cm

C) 390 and 400 cm

D) None of these

Correct Answer: A

Solution :

Let common radius be r cm.

Then, height of cylinder = h

and height of cone = h'

\[\therefore \]Volume of the structure = Volume of (cone + cylinder + hemisphere)

\[=\frac{1}{3}\pi {{r}^{2}}{{h}_{1}}+\pi {{r}^{2}}{{h}_{2}}+\frac{2\pi {{r}^{3}}}{3}\]

\[=\frac{1}{3}\pi [{{(3.5)}^{2}}\times 2.8+3\times {{(3.5)}^{2}}\times 6.5+2\times {{(35)}^{3}}]\]

\[=\frac{1}{3}\times \frac{22}{7}[{{(3.5)}^{2}}\times (2.8+3\times 6.5+2\times 3.5)]\] \[=\frac{1}{3}\times \frac{22}{7}\times \frac{35}{10}\times \frac{35}{10}(29.3)=376.01\]