Advertisements
Advertisements
प्रश्न
A right-angled triangle whose sides are 6 cm, 8 cm and 10 cm is revolved about the sides containing the right angle in two ways. Find the difference in volumes of the two solids so formed.
उत्तर
Three sides of a triangle are 6 cm, 8 cm and 10 cm.
Case (i): If the triangle is revolved about the side 6 cm, the cone will be formed with radius 6 cm and height 8 cm.
Volume of the cone = `1/3 pi"r"^2"h"` cu. units
= `1/3 xx pi xx 6 xx 6 xx 8`
= 96π cm3
Case (ii): If the triangle is revolved about the side 8 cm, the cone will be formed with radius 8 cm and height 6 cm.
Volume of the cone = `1/3 xx pi xx 8 xx 8 xx 6`
= 128π cm3
Difference in volume of the two solids
= (128π – 96π) cm3
= 32π cm3
= `32 xx 22/7` cm3
= 100.57 cm3
The difference in the volume of the two solids = 100.57 cm3
APPEARS IN
संबंधित प्रश्न
How much iron is needed to make a rod of length 90 cm and diameter 1.4 cm?
The height of a circular cylinder is 20 cm and the radius of its base is 7 cm. Find : the total surface area.
A cylinder of circumference 8 cm and length 21 cm rolls without sliding for `4 1/2` seconds at the rate of 9 complete rounds per second. Find the area covered by the cylinder in `4 1/2` seconds.
A metal container in the form of a cylinder is surmounted by a hemisphere of the same radius. The internal height of the cylinder is 7 m and the internal radius is 3.5 m. Calculate: the internal volume of the container in m3.
Find the weight of a lead pipe 35 cm long. The external diameter of the pipe is 2.4 cm and the thickness of the pipe is 2mm, given 1 cm3 of lead weighs 10 gm.
A rectangular paper of width 14 cm is rolled along its width and a cylinder of radius 20 cm is formed. Find the volume of the cylinder. (Take `22/7` for π)
Collect some old postcards. You can also use thick paper of size 14 cm x 9 cm.
Fold the postcard along the width to make pipe 1. Join the ends with cello tape.
Take another postcard and fold it along the length to make pipe 2. Join the ends with tape.
- Guess which pipe can take more sand inside it. Hold it on a plate and pour sand to check your guess. Was your guess correct? Discuss.
The total surface area of a cone whose radius is `r/2` and slant height 2l is ______.
The volume of the largest right circular cone that can be fitted in a cube whose edge is 2r equals to the volume of a hemisphere of radius r.
Two cylinders A and B are formed by folding a rectangular sheet of dimensions 20 cm × 10 cm along its length and also along its breadth respectively. Then volume of A is ______ of volume of B.
