Advertisements
Advertisements
Question
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.
Advertisements
Solution
Given that,
Length of cylindrical part = 7 m
Radius of cylindrical part = `7/2` m
Total surface area of figure = 2πrh + 2(2πr2)
= `2π[7/2 xx 7 + 2 xx (7/2)^2]`
= 308 m2
Volume of boiler = Volume of cylindrical part + Volume of two hemispherical parts
= `πr^2h + (4/3)πr^3`
= `π(7/2)^2 xx (7) + (4/3)π(7/2)^3`
= 269.5 + 179.66
= 449.167 m3
Required Ratio = `"Volume of cylindrical part"/"Volume of one hemispherical part"`
= `269.5/89.83`
= 3
RELATED QUESTIONS
In Fig. 5, from a cuboidal solid metallic block, of dimensions 15cm ✕ 10cm ✕ 5cm, a cylindrical hole of diameter 7 cm is drilled out. Find the surface area of the remaining block [Use
`pi=22/7`]
Find the area of the shaded region in Fig. 3, where arcs drawn with centres A, B, C and D intersect in pairs at mid-points P, Q, R and S of the sides AB, BC, CD and DA respectively of a square ABCD of side 12 cm. [Use π = 3.14]
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 metallic cylinder has radius 3 cm and height 5 cm. To reduce its weight, a conical hole is drilled in the cylinder. The conical hole has a radius of `3/2` cm and its depth is `8/9 `cm. Calculate the ratio of the volume of metal left in the cylinder to the volume of metal taken out in conical shape.
A solid sphere of radius r is melted and cast into the shape of a solid cone of height r, the radius of the base of the cone is
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)
Five identical cubes, each of edge 5 cm, are placed adjacent to each other. Find the volume of the resulting cuboid.
Find the ratio of the volume of a cube to that of a sphere which will fit inside it.
The radius of spherical balloon increases from 8 cm to 12 cm. The ratio of the surface areas of balloon in two cases 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 ______.
