Question

If the radius height of a cone are in the ratio 5 : 12 and its volume is $314c{m}^3$ then slant height is

• A. 12 cm
• B. 10 cm
• C. 13 cm
• D. 15 cm

Answer 1

The correct option is C 13 cm

Let the radius and height of cone is $5x$ and $12x$

$\therefore \frac{1}{3}\times 3.14\times (5x{)}^2\times (12x)=314$

$\frac{1}{3}\times 3.14\times 25x^2\times 12x=314$

$x^3=1$

$x=1$

Height is $5$ cm and radius is $12$ cm,

Then slant height $=\sqrt{(12{)}^2+(5{)}^2}$

$=\sqrt{144+25}$

$=\sqrt{169}$

$=13$ cm