Question

The diameter of the base of metallic cone is $2$ cm and height is $10$ cm. $900$ such cones are molten to form 1 right circular cylinder whose radius is $10$ cm. Find total surface area of the right circular cylinder so formed. (Given $\pi$ = 3.14)

• A. $2510$ c$m^2$
• B. $2512$ $c{m}^2$
• C. $2515$ $c{m}^2$
• D. $2530$ $c{m}^2$

Answer 1

The correct option is B $2512$ $c{m}^2$

Diameter of the base of metallic cone $=2$ cm
Its radius $=$ $\frac{2}{2}$ $=$ $1$ cm
Its height $=$ $10$ cm
Volume of metallic cone $=$ $\frac{1}{3}\pi r^{2}h$
$=$ $\frac{1}{3}\pi \times 1\times 1\times 10$
$=$ $\frac{10\pi }{3}c{m}^3$
$\therefore$ volume of $900$ metallic cones $=$ $900\times \frac{10\pi }{3}c{m}^3$ $=$ $3000\pi c{m}^3$
$900$ cones are melted to form a right circular cylinder.
$\therefore$ volume of a cylinder $=$ $3000\pi$
For a cylinder, radius $\left(r_2\right)=10$ cm
and height be $\left(h_2\right)$
$\therefore$ volume of a cylinder $=$ $\pi r_1^2{h}_1$
$\therefore 3000\pi =\pi \times 10\times 10h_2$
$\therefore h_1=30$ cm
Total surface area of cylinder $=$ $2\pi r_1(r_1+h_1)$
$=$ $23.1410(10+30)$
$=$ $6.281040$
$=$ $2512c{m}^2$
$\therefore$ total surface area of the right circular cylinder is $2512c{m}^2$.