In the previous section, we have discussed how to find the surface area of solids made up of a combination of two basic solids. Here, we shall see how to calculate their volumes.
Volume of combination can be found out by adding volumes of different solids or by subtracting volumes of different solids.
Example 1- Shanta runs an industry in a shed which is in the shape of a cuboid surmounted by a half cylinder. If the base of the shed is of dimension 7 m × 15 m, and the height of the cuboidal portion is 8 m, find the volume of air that the shed can hold. Further, suppose the machinery in the shed occupies a total space of `300 m^3`, and there are 20 workers, each of whom occupy about `0.08 m^3` space on an average. Then, how much air is in the shed? `(Take pi= 22/7)`
Solution- Volume of air in shed= Volume of shed- Space occupied by workers and machinery
Volume of shed= Volume of cuboid+ Volume of half cylinder
`= (8 xx 7 xx 15)+ 1/2 pi r^2h`
= `(8 xx 7 xx 15)+ 1/2 xx 22/7 xx (7/2)^2 xx 15`
Volume of shed =`1128.75 cm^3`
Volume of air in shed= Volume of shed- Space occupied by workers and machinery
`= 1128.75- 300+ (20 xx 0.08)`
Volume of air in shed= `827.15 m^3`
Example 2- A juice seller was serving his customers using glasses. The inner diameter of the cylindrical glass was 5 cm, but the bottom of the glass had a hemispherical raised portion which reduced the capacity of the glass. If the height of a glass was 10 cm, find the apparent capacity of the glass and its actual capacity. (Use π = 3.14.)
Solution: Capacity of the glass= Volume of glass- Volume of hemisphere
= `pi r^2h -2/3 pi r^3`
= `[3.14 (2.5)^2 xx 10] -[2/3 xx 3.14 xx (2.5)^3]`
`"Capacity of the glass"= 163.54 cm^3`
In the equilateral Δ ABC of side 14 cm, side BC is the diameter of a semicircle as shown in the figure below. Find the area of the shaded region. (Take π = 22/7 and √3 = 1.732)
The boundary of the shaded region in the given diagram consists of three semicircular areas, the smaller ones being equal and it’s diameter 5 cm, if the diameter of the larger one is 10 cm,
(i) The length of the boundary,
(ii) The area of the shaded region. (Take π = 3.14)
In the given figure, AB is the diameter of a circle with center O and OA = 7 cm. Find the area of the shaded region.
Find the perimeter and area of the shaded portion of the following diagram; give your answer correct to 3 significant figures. (Take π = 22/7).
A well 28.8 m deep and of diameter 2 m is dug up. The soil dug out is spread all around the well to make a platform 1 m high considering the fact losse soil settled to a height in the ratio 6 : 5 find the width of the platform.
A circus tent is cylindrical to a height of 3 meters and conical above it. If its diameter is 105 m and the slant height of the conical portion is 53 m calculate the length of the canvas which is 5m wide to make the required tent.
An iron pillar has some part in the form of a right circular cylinder and remaining in the form of a right circular cone. The radius of the base of each of cone and cylinder is 8 cm. The cylindrical part is 240 cm high and the conical part is 36 cm high. Find the weight of the pillar if one cubic cm of iron weight is 7.8 grams.