Advertisements
Advertisements
Question
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 the canvas required in m2 is
Options
1760
2640
3960
7920
Advertisements
Solution
For conical portion
` r = 52 .5m and l = 40m`
Curved surface area of the conical portion
`= pirl`
`=pi xx 52.5 xx 40`
`= 2100 pi m^2`
For cylindrical portion we have
r = 52.5m and h =4m
Then,
Curved surface area of cylindrical portion
`=2pirh`
`=2 xx pi xx 52.5 xx 4`
` = 420 pi m^2`
Area of canvas used for making the tent
`= (2100m + 420)pi`
`=2520 xx 22/7`
`= 7920m^2`
RELATED QUESTIONS
In Fig. 5, is a decorative block, made up two solids – a cube and a hemisphere. The base of the block is a cube of side 6 cm and the hemisphere fixed on the top has diameter of 3.5 cm. Find the total surface area of the bock `(Use pi=22/7)`
2 cubes each of volume 64 cm3 are joined end to end. Find the surface area of the resulting cuboid.
A medicine capsule is in the shape of cylinder with two hemispheres stuck to each of its ends (see the given figure). The length of the entire capsule is 14 mm and the diameter of the capsule is 5 mm. Find its surface area. [Use π = `22/7`]
If the radii of circular ends of a bucket 24cm high are 5cm and 15cm. find surface area of
bucket?
If the radius of the base of a right circular cylinder is halved, keeping the height the same, then the ratio of the volume of the cylinder thus obtained to the volume of original cylinder is:
The largest cone is curved out from one face of solid cube of side 21 cm. Find the volume of the remaining solid.
Find the volume of a solid in the form of a right circular cylinder with hemi-spherical ends whose total length is 2.7 m and the diameter of each hemi-spherical end is 0.7 m.
Two solid cones A and B are placed in a cylindrical tube as shown in fig .16.76. The ratio of their capacities are 2: 1 . Find the heights and capacities of the cones . Also, find the volume of the remaining portion of the cylinder.
The volume of a hemisphere is 2425 `1/2` cm3 . Find its curved surface area.
A cubical block of side 10 cm is surmounted by a hemisphere. What is the largest diameter that the hemisphere can have? Find the cost of painting the total surface area of the solid so formed, at the rate of ₹ 5 per 100 sq cm. [Use π = 3.14.]
A right triangle whose sides are 15 cm and 20 cm (other than hypotenuse), is made to revolve about its hypotenuse. Find the volume and surface area of the double cone so formed. (Choose value of π as found appropriate)
Three metallic cubes whose edges are 3 cm, 4 cm and 5 cm, are melted and recast into a single large cube. Find the edge of the new cube formed.
Match the following columns:
| Column I | Column II |
| (a) The radii of the circular ends of a bucket, in the form of the 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 20 and 12 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 spheres 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 |
A cone of height 24 cm and radius of base 6 cm is made up of modelling clay. A child reshapes it in the form of a sphere. Find the radius of the sphere and hence find the surface area of this sphere.
The total surface area of a solid hemisphere of radius r is ________.
If two solid hemispheres of the same base radius r are joined together along their bases, then curved surface area of this new solid is ______.
Two cones with same base radius 8 cm and height 15 cm are joined together along their bases. Find the surface area of the shape so formed.
A tent is in the shape of a cylinder surmounted by a conical top. If the height and radius of the cylindrical part are 3 m and 14 m respectively, and the total height of the tent is 13.5 m, find the area of the canvas required for making the tent, keeping a provision of 26 m2 of canvas for stitching and wastage. Also, find the cost of the canvas to be purchased at the rate of ₹ 500 per m2.
The ratio of total surface area of a solid hemisphere to the square of its radius is ______.
