A tent is in the form of a right circular cylinder surmounted by a con

1.	A tent is in the form of a right circular cylinder surmounted by a cone. The diameter of cylinder is 24 m. The height of the cylindrical portion is 11 m while the vertex of the cone is 16 m above the ground. Find the area of the canvas required for the tent.
Answer» For cylindrical part, we have Diameter = 24 m So, radius r = 24/2 = 12m, Height = h = 11m For conical part, we have Height of the cone = (16-11)m = 5m ∴ Slant height = \(\sqrt{12^2+5^2}\) m = 13 m Hence, Area of the canvas required = Curved surface area of cone + Curved surface area of cylinder = πrl + 2πrh = πr(l+2h) = \(\frac{22}{7}\) ×12 × (13 + 22) m² = 1320 m²

A tent is in the form of a right circular cylinder surmounted by a cone. The diameter of cylinder is 24 m. The height of the cylindrical portion is 11 m while the vertex of the cone is 16 m above the ground. Find the area of the canvas required for the tent.

Answer»

For cylindrical part, we have

Diameter = 24 m

So,

radius r = 24/2 = 12m,

Height = h = 11m

For conical part, we have

Height of the cone = (16-11)m = 5m

∴ Slant height = \(\sqrt{12^2+5^2}\) m

= 13 m

Hence,

Area of the canvas required

= Curved surface area of cone + Curved surface area of cylinder

= πrl + 2πrh = πr(l+2h)

= \(\frac{22}{7}\) ×12 × (13 + 22) m²

= 1320 m²