Advertisements
Advertisements
Question
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
Solution
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
RELATED QUESTIONS
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)
From a solid cylinder whose height is 2.4 cm and diameter 1.4 cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid to the nearest cm2
[use `pi = 22/7`]
A tent of height 77dm is in the form a right circular cylinder of diameter 36m and height 44dm surmounted by a right circular cone. Find the cost of canvas at Rs.3.50 per m2 ?
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 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
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.
From a solid cube of side 7 cm , a conical cavity of height 7 cm and radius 3 cm is hollowed out . Find the volume of the remaining solid.
Two cubes each of volume 27 cm3 are joined end to end to form a solid. Find the surface area of the resulting cuboid.
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?
In a right circular cone, the cross-section made by a plane parallel to the base is a
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.
A container opened at the top and made up of a metal sheet, is in the form of a frustum of a cone of height 16 cm with radii of its lower and upper ends as 8 cm and 20 cm respectively. Find the cost of milk which can completely fill the container, at the rate of ₹ 50 per litre. Also find the cost of metal sheet used to make the container, if it costs ₹ 10 per 100 cm2. (Take π = 3⋅14)
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 ______.
A plumbline (sahul) is the combination of (see figure) ______.
The total surface area of a solid hemisphere of radius 7 cm is ______.
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.
Statement A (Assertion): Total Surface area of the top is the sum of the curved surface area of the hemisphere and the curved surface area of the cone.
Statement R( Reason): Top is obtained by joining the plane surfaces of the hemisphere and cone together.
