Question

The canvas required to construct a cone of height $24$ m and base radius $7$ m is:

• A. $500$ ${\text{m}}^2$
• B. $520$ ${\text{m}}^2$
• C. $550$ ${\text{m}}^2$
• D. None of these

Answer 1

Answer: (C)

$550$ ${\text{m}}^2$

Given, the height of cone $h=24m$ and base radius is $r=24m$.

Then, slant height $l=\sqrt{r^2+h^2}$

$=\sqrt{(24{)}^2+(7{)}^2}$

$=\sqrt{576+49}$

$=\sqrt{625}=25$.

Now, canvas required to construct cone $=$ the curved surface area of cone

$=\pi rl$

$=\frac{22}{7}\times 7\times 25$

$=550m^2$.

Hence, option $C$ is correct.