We have already learnt about the surface area and volumes of figures, but in this chapter we will given different combinations of solids. We are known with solids like cylinder, sphere, cone, cuboid, rectangle, square, etc. In this chapter we are suppose to find surface areas of different combinations of solids.
Now before we proceed, we must understand what is curved surface area. The solids having curved surface are cone, cylinder. Curved surface area is the outer portion, the area of flat ends of such solids will not be included while calculating Curved surface area. But while calculating Total surface area we must include the area of flat ends of the solids, provided that the solid should not be hollow from inside.
Example- 2 cubes each of volume `64 cm^3` are joined end to end. Find the surface area of the resulting cuboid.
Solution- `Volume of cube= 64cm^3`
`"edge of cube"` = `3 sqrt 64` cm
edge= 4 cm
By adding this two cube we get a cuboid
So we get dimensions of cuboid as
As we have two cube the lenght will be doubled
therefore, lenght = 2(4)= 8cm
Surface area of cuboid= 2 (lb+bh+hl)
= `2 (8 xx 4)+(4 xx 4)+(4 xx 8
=` 2 (32+16+32)`
= `2 (80)`
Surface area of cuboid= `160 cm^2`
Shaalaa.com | Surface Area and Volume part 3 (Surface Area Examples)
Series 1: playing of 8
A test tube has diameter 20 mm and height is 15 cm. The lower portion is a hemisphere. Find the capacity of the test tube. (π = 3.14)
The sum of length, breadth and height of a cuboid is 38 cm and the length of its diagonal is 22 cm. Find the total surface area of the cuboid.
A farmer connects a pipe of internal diameter 20 cm from a canal into a cylindrical tank which is 10 m in diameter and 2 m deep. If the water flows through the pipe at the rate of 4 km per hour, in how much time will the tank be filled completely?
Water flows at the rate of 15 m per minute through a cylindrical pipe, having the diameter 20 mm. How much time will it take to fill a conical vessel of base diameter 40 cm and depth 45 cm?
The radius and slant height of a cone are 5 cm and 20 cm respectively. Find its curved surface area. (Π = 3.14)