Advertisements
Advertisements
प्रश्न
A wooden toy is in the shape of a cone mounted on a cylinder, as shown in the figure. The total height of the toy is 26 cm, while the height of the conical part is 6 cm. The diameter of the base of the conical part is 5 cm and that of the cylindrical part is 4 cm. The conical part and the cylindrical part are respectively painted red and white. Find the area to be painted by each of these colours. `["Take" pi = 22/7]`
Advertisements
उत्तर
we have,
the base radius of the conical part, r = 5/2= 2.5 cm,
the base radius of the cylindrical part, R = 4/2 = 2 cm
the total height of the toy = 26 cm,
the height of the conical part, h = 6 cm
Also, the height of the cylindrical part , H=26-6 = 20 cm
And, the slant height of the conical part, `l = sqrt(r^2+ h^2) = sqrt (2.5^2+6^2) = sqrt(6.25+36)=sqrt(42.25) = 6.5 cm `
Now,
The area to be painted by red colour = CSA of cone + Area of base of conical part -Area base of cylinderical part
`= pirl+pir^2-piR^2`
`= 22/7xx2.5xx6.5+22/7xx2.5xx2.5-22/7xx2xx2`
`=22/7xx 16.25 +22/7xx6.25- 22/7xx4`
`= 22/7xx(16.25+6.25-4)`
`=22/7xx18.5`
≈ 58.14 cm2
Also,
The area to be painted by white colour = CSA of cylinder + Area of base of cylinder
`= 2piRH + piR^2`
`=piR(2H+R)`
`=22/7xx2xx(2xx20+2)`
`=22/7xx2xx42`
= 264 cm2
APPEARS IN
संबंधित प्रश्न
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 Rs. 5 per 100 sq. cm. [Use π = 3.14]
A toy is in the form of a cone of base radius 3.5 cm mounted on a hemisphere of base diameter 7 cm. If the total height of the toy is 15.5 cm, find the total surface area of the top (Use π = 22/7)
A solid is in the form of a right circular cylinder, with a hemisphere at one end and a cone at the other end. The radius of the common base is 3.5 cm and the heights of the cylindrical and conical portions are 10 cm. and 6 cm, respectively. Find the total surface area of the solid. (Use π =`22/7`)
A toy is in the shape of a right circular cylinder with a hemisphere on one end and a cone on the other. The radius and height of the cylindrical part are 5 cm and 13 cm respectively.The radii of the hemispherical and conical parts are the same as that of the cylindrical part.Find the surface area of the toy if the total height of the toy is 30 cm.
A bucket has top and bottom diameter of 40 cm and 20 cm respectively. Find the volume of the bucket if its depth is 12 cm. Also, find the cost of tin sheet used for making the bucket at the rate of Rs. 1.20 per dm2 . (Use π = 3.14)
A bucket made of aluminum sheet is of height 20cm and its upper and lower ends are of radius 25cm an 10cm, find cost of making bucket if the aluminum sheet costs Rs 70 per
100 cm2
Radii of circular ends of a solid frustum off a cone re 33cm and 27cm and its slant height are 10cm. find its total surface area?
A milk container is made of metal sheet in the shape of frustum of a cone whose volume is 10459 `3/7` cm3. The radii of its lower and upper circular ends are 8cm and 20cm. find the cost of metal sheet used in making container at rate of Rs 1.4 per cm2?
Find the number of metallic circular discs with a 1.5 cm base diameter and of height 0.2 cm to be melted to form a right circular cylinder of height 10 cm and diameter 4.5 cm.
How many spherical lead shots each of diameter 4.2 cm can be obtained from a solid rectangular lead piece with dimension 6cm \[\times\] 42cm \[\times\] 21 cm.
The inner and outer radii of a hollow cylinder are 15 cm and 20 cm, respectively. The cylinder is melted and recast into a solid cylinder of the same height. Find the radius of the base of new cylinder.
In a village, a well with 10 m inside diameter, is dug 14 m deep. Earth taken out of it is spread all around to a width 5 m to form an embankment. Find the height of the embankment. What value of the villagers is reflected here?
How many cubes of 10 cm edge can be put in a cubical box of 1 m edge?
If the areas of three adjacent faces of a cuboid are x, y and z, respectively, the volume of the cuboid is ______.
The radius of spherical balloon increases from 8 cm to 12 cm. The ratio of the surface areas of balloon in two cases is ______.
The total surface area of a solid hemisphere of radius r is ________.
The shape of a gilli, in the gilli-danda game (see figure), is a combination of ______.
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.
The boilers are used in thermal power plants to store water and then used to produce steam. One such boiler consists of a cylindrical part in middle and two hemispherical parts at its both ends.
Length of the cylindrical part is 7 m and radius of cylindrical part is `7/2` m.
Find the total surface area and the volume of the boiler. Also, find the ratio of the volume of cylindrical part to the volume of one hemispherical part.
