A conical tent is 6 m high and the radius of its base is 8 m. Find:

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Here are the solutions for the conical tent problem:

A conical tent is 6 m high and the radius of its base is 8 m. Find:

a) slant height of the tent.

b) cost required to make the tent, if the cost of 1 m $^2$ canvas is Birr 250.
Use $\pi = 3.14$ .

a) Slant height of the tent

Identify the given values for height ( $h$ ) and radius ( $r$ ).
$h = 6 \text{ m}$ $r = 8 \text{ m}$
Use the Pythagorean theorem to find the slant height ( $l$ ).
$l = \sqrt{r^2 + h^2}$ $l = \sqrt{(8 \text{ m})^2 + (6 \text{ m})^2}$ $l = \sqrt{64 \text{ m}^2 + 36 \text{ m}^2}$ $l = \sqrt{100 \text{ m}^2}$ $l = 10 \text{ m}$
The slant height of the tent is $\boxed{\text{10 m}}$ .

b) Cost required to make the tent
Calculate the lateral surface area ( $LSA$ ) of the cone, which represents the canvas needed for the tent.
The formula for the lateral surface area of a cone is $LSA = \pi r l$ .
$LSA = (3.14) (8 \text{ m}) (10 \text{ m})$ $LSA = 3.14 \times 80 \text{ m}^2$ $LSA = 251.2 \text{ m}^2$
Calculate the total cost by multiplying the lateral surface area by the cost per square meter.
Cost per 1 m $^2$ = Birr 250.
Total Cost = $LSA \times \text{Cost per m}^2$
Total Cost = $251.2 \text{ m}^2 \times \text{Birr } 250/\text{m}^2$
Total Cost = Birr 62800
The cost required to make the tent is $\boxed{\text{Birr 62800}}$ .

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