Surface Areas and Volumes — Question 4

(i) Given,

Radius of conical tent (r) = 24 m

Height of conical tent (h) = 10 m

By formula,

Slant height of conical tent (l) = $\sqrt{r^2 + h^2}$

Substituting values we get :

$l = \sqrt{(24)^2 + (10)^2} \\[1em] = \sqrt{576 + 100} \\[1em] = \sqrt{676} = 26 \text{ m}$

Hence, slant height of the conical tent is 26 m.

(ii) Given,

Curved surface area of the cone = πrl

= $\dfrac{22}{7}$ × 24 × 26

= $\dfrac{13728}{7}$ m²

The cost of the canvas required to make the tent, at ₹ 70 per m² = Curved surface area of the cone x ₹ 70

= $\dfrac{13728}{7}$ × 70

= ₹ 137280.

Hence, the cost of the canvas is ₹ 137280.