Question

The volume of a conical tent is 2156m³ and the area of its floor is 616m². Calculate :i) The height of the cone.ii) The radius of its base.iii) The length of canvas required to cover the tent if the width of canvas is 2m.

Answer 1

Answer:

(i) 10.5 m (ii) 14 m (iii) 385 m

Step-by-step explanation:

Find the height of the cone:

Volume = 2156 m³

Floor Area = 616 m²

Volume = 1/3 base area x height

2156 = 1/3  x 616 x height

616 x height = 6468

height = 6468 ÷ 616 = 10.5 m

Find the radius of the base:

Area = πr²

616 = πr²

r² = 616 ÷ π

r² = 196

r = √196

r = 14 m

Find the slanted height of the tent:

a² + b² = c²

c² = 14² + 10.5²

c² = 306.25

c = √306.25

c = 17.5 m

Find the surface area of the canvas:

Surface area = πrl

Surface area = π(14)(17.5) = 770 m²

Find the length of the canvas:

Length = Area ÷ Breadth

Length = 770 ÷ 2 = 385 m

Answer: (i) 10.5 m (ii) 14 m (iii) 385 m