Advertisements
Advertisements
प्रश्न
A right circular cone and a right circular cylinder have equal base and equal height. If the radius of the base and height are in the ratio 5 : 12, write the ratio of the total surface area of the cylinder to that of the cone.
उत्तर
Given that
r : h = 5 :12
i.e. r = 5x , h =12x
Since,
Right, circular cone and right circular cylinder have equal base and equal right.
Therefore,
The total surface area of cylinder `S_1 = 2pir (h + r)`
The total surface area of cone `S_2 = pir(l + r)`
`l = sqrt(r^2 + h^2)`
`= sqrt(25x^2 + 144x^2)`
`=sqrt(169x^2)`
`l = 13x`
Now,
`S_1/S_2 = (2pir(h + r))/(pir (l +r))`
`= (2(h+r))/(l+r)`
`S_1 /S_2 = (2(12x + 5x))/(13x + 5x)`
`=(2xx 17x)/(18x)`
`S_1 /S_2 = 17/9`
Hence,`S_1 : S_2 = 17 : 9`
APPEARS IN
संबंधित प्रश्न
The slant height of a frustum of a cone is 4 cm and the perimeters (circumference) of its circular ends are 18 cm and 6 cm. find the curved surface area of the frustum.
A bucket, made of metal sheet, is in the form of a cone whose height is 35 cm and radii of circular ends are 30 cm and 12 cm. How many litres of milk it contains if it is full to the brim? If the milk is sold at Rs 40 per litre, find the amount received by the person.
The radii of the circular ends of a frustum are 6 cm and 14 cm. If its slant height is 10 cm, then its vertical height is
A bucket made up of a metal sheet is in the form of a frustum of a cone of height 16 cm and radii of its lower and upper ends are 8 cm and 20 cm, respectively. Find the cost of the bucket if the cost of metal sheet used is Rs 15 per 100 cm2.
A cone is cut by a plane parallel to its base and the upper part is removed. The part that is left is called
A shuttlecock used for playing badminton has the shape of the combination of ______.
The radii of the top and bottom of a bucket of slant height 13 cm are 9 cm and 4 cm respectively. The height of the bucket is ______.
A cone is cut through a plane parallel to its base and then the cone that is formed on one side of that plane is removed. The new part that is left over on the other side of the plane is called ______.
The diameters of the two circular ends of the bucket are 44 cm and 24 cm. The height of the bucket is 35 cm. The capacity of the bucket is ______.
Read the following passage and answer the questions given below.
|
A 'circus' is a company of performers who put on shows of acrobats, clowns etc. to entertain people started around 250 years back, in open fields, now generally performed in tents. One such 'Circus Tent' is shown below. The tent is in the shape of a cylinder surmounted by a conical top. If the height and diameter of cylindrical part are 9 m and 30 m respectively and height of conical part is 8 m with same diameter as that of the cylindrical part, then find |
- the area of the canvas used in making the tent;
- the cost of the canvas bought for the tent at the rate ₹ 200 per sq m, if 30 sq m canvas was wasted during stitching.
