Question

For finding total surface area of cone, which of the given expressions are required?
(I) The area of the base of the cone is $1386c{m}^2$.
(II) The curved surface area of the cone is $2310c{m}^2$.
(III) The volume of the cone is $3696c{m}^3$.

• A. I and either II or III
• B. II and either I or III
• C. III and either or I or II
• D. Any two of the three

Answer 1

Answer: (D)

Any two of the three

Statement (I):
Area of base$=1386c{m}^2$
$⟹$ $\pi r^2=1386c{m}^2$.

Statement (II):
Curved surface area$=2310c{m}^2$
$⟹$ $\pi rl$ $=\pi r\sqrt{r^2+h^2}$.

Statement (III):
Volume of cone$=3696c{m}^3$
$⟹$ $\frac{1}{3}\pi r^{2}h=3696c{m}^3$.

For total surface area $=\pi r^2+\pi rl$
$=\pi r^2+\pi r\sqrt{h^2+r^2}$.

As it is dependent on $r$ and $h$, and it can be solved using any of two statements.

Hence, any two of the three statements can be used.