Question

A hut has cylindrical base with radius 7 m and conical top of height 3 m. The total height of the hut is 7 m. Then the Curved surface area of the hut is ____

• A. $176+22\sqrt{58}{\text{m}}^2$
• B. $176+\sqrt{58}{\text{m}}^2$
• C. $88+22\sqrt{58}{\text{m}}^2$
• D. $88+\sqrt{58}{\text{m}}^2$

Answer 1

The correct option is A $176+22\sqrt{58}{\text{m}}^2$

Given:
Radius, r = 7 m
Height of Cone, h = 3 m
Height of Cylinder = 7 - 3 = 4 m

Curved surface area of Hut
= CSA of Cylinder + CSA of Cone

CSA of Cylinder
$=2\pi rh=2\times \frac{22}{7}\times 7\times 4=176{\text{m}}^2$

CSA of Cone
$=\pi rl$

Length of cone,
$l=\sqrt{r^2+h^2}=\sqrt{7^2+3^2}=\sqrt{49+9}=\sqrt{58}{\text{m}}^2$

CSA of Cone
$=\frac{22}{7}\times 7\times \sqrt{58}=22\sqrt{58}{\text{m}}^2$

Curved surface area of Hut
$=176+22\sqrt{58}{\text{m}}^2$