Q73 of 227 Page 917

A circus tent is cylindrical to a height of 4 m and conical above it. If its diameter is 105 m and its slant height is 40 m, the total area of canvas required is

Given: A circus tent is cylindrical to a height of 4 m and conical above it.

Its diameter is 105 m and its slant height is 40 m.

CSA of the Cylinder is given by: 2πrh (here, r and h are radius and height respectively)

Let V₁ be the CSA of the cylindrical part of tent

∴ V₁ = 2πrh

⇒ V₁ = 2 × π × × 4 = 1320cm² (here diameter is 105 cm, ∴ radius = cm)

CSA of the cone is given by: πrl (here, r and l are radius and slant height respectively)

Let V₂ be the CSA of the conical part of tent

∴ V₂ = πrl

⇒ V₂ = π × × 40 = 6600 cm² (here diameter is 105 cm, ∴ radius = cm)

∴ Total area of the canvas is V₁ + V₂

∴ V₁ + V₂ = 1320 + 6600 = 7920cm²

∴ Total area of the canvas is: 7920 cm²

The circular ends of a bucket are of radii 35 cm and 14 cm and the height of the bucket is 40 cm. Its volume is

If the radii of the end of a bucket are 5 cm and 15 cm and it is 24 cm high then its surface area is (use π = 3.14)

Match the following columns:

Column I	Column II
(a) A solid metallic sphere of radius 8 cm is melted and the material is used to make solid right cones with height 4 cm and radius of the base 8 cm. How many cones are formed?	(p) 18
(b) A 20-m-deep well with diameter 14 m is dug up and the earth from digging is evenly spread out to form a platform 44 m by 14 m. the height of the platform is…..m.	(q) 8
(c) A sphere of radius 6 cm is melted and recast into the shape of a cylinder of radius 4 cm. then the height of the cylinder is ….. cm.	(r) 16:9
(d) The volumes of two sphere are in the ratio 64:27. The ratio of their surface areas is ….. .	(s) 5

Match the following columns:

Column I	Column II
(a) The radii of the circular ends of a bucket in the form of frustum of a cone of height 30 cm are 20 cm and 10 cm respectively. The capacity of the bucket is ….. cm³. [Take π = 22/7]	(p) 2418π
(b) The radii of the circular ends of a conical bucket of height 15 cm are 28 and 20 cm respectively. The slant height of the bucket is …. cm.	(q) 22000
(c) The radii of the circular ends of a solid frustum of a cone are 33 cm and 27 cm and its slant height is 10 cm. The total surface area of the bucket is …. Cm².	(r) 12
(d) Three solid metallic sphere of radii 3 cm, 4 cm and 5 cm are melted to form a single solid sphere. The diameter of the resulting sphere is … cm.	(s) 17