Question

Find the slant height and vertical height of a cone with radius 5.6 cm and curved surface area 158.4$c{m^2}$.
A. 8.07 cm
B. 7.05 cm
C. 8 cm
D. None of the above

Answer 1

Hint: In these type of questions we need to remember the basic formulae of solid figures and the relation between the radius, vertical and slant height of the cone, i.e. ${l^2} = {r^2} + {h^2}$. And we will use the formula i.e. curved surface area of cone = $\pi rl$

Complete step-by-step answer:

Given,
Radius of the cone=5.6 cm
Curved surface area of cone = 158.4$c{m^2}$
We know that, curved surface area of cone = $\pi rl$
$
  158.4 = \dfrac{{22}}{7} \times (5.4) \times l \\
  l = 158.4 \times \dfrac{7}{{22}} \times \dfrac{1}{{(5.4)}} \\
  l = 9.3cm \\
 $
Now, using the relation ${l^2} = {r^2} + {h^2}$
$
  {(9.3)^2} = {(5.4)^2} + {h^2} \\
  h = \sqrt {{{(9.3)}^2} - {{(5.4)}^2}} \\
  h = \sqrt {57.33} \\
  h = 7.5cm \\
 $
Here, the slant height and vertical height are 9.3cm and 7.5 cm respectively.
Hence, the answer to this question is None of the above.

So, the correct answer is “Option D”.

Note: Whenever you get to solve such problems you need to recall the formula of the curved surface area of the cone and try to find the values of variables in the formula if the values are not given with the help of the information provided. doing this will solve all such problems and you will get the right answer.