Advertisements
Advertisements
प्रश्न
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.
विकल्प
True
False
उत्तर
This statement is True.
Explanation:
Given, edge of cube = 2r, then height of cube becomes h = 2r.
Volume of a cone = `1/3 pir^2h = 1/3 pir^2(2r) = 2/3 pir^3`
Volume of a hemisphere = `2/3 pir^3`
Hence, the volume of a cone is equal to the volume of a hemisphere.
APPEARS IN
संबंधित प्रश्न
An exhibition tent is in the form of a cylinder surmounted by a cone. The height of the tent above the ground is 85 m and height of the cylindrical part of 50 m. If the diameter of the base is 168 m, find the quantity of canvas required to make the tent. Allow 20% extra for fold and for stitching. Give your answer to the nearest m2.
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 distance travelled by the cylinder in `4 1/2` seconds.
What length of solid cylinder 2 cm in diameter must be taken to recast into a hollow cylinder of external diameter 20 cm, 0.25 cm thick and 15 cm long?
Two right circular solid cylinders have radii in the ratio 3 : 5 and heights in the ratio 2 : 3. Find the ratio between their volumes.
A glass cylinder with a diameter 20 cm has water to a height of 9 cm. A metal cube of 8 cm edge is immersed in it completely. Calculate the height by which the water will up in the cylinder. Answer correct of the nearest mm. (Take π = 3.142)
The total surface area of a cone whose radius is `r/2` and slant height 2l is ______.
30 circular plates, each of radius 14 cm and thickness 3 cm are placed one above the another to form a cylindrical solid. Find volume of the cylinder so formed.
Two cylinders of equal volume have heights in the ratio 1 : 9. The ratio of their radii is ______.
Radius of a cylinder is r and the height is h. Find the change in the volume if the height is doubled.
A rectangular sheet of paper is rolled in two different ways to form two different cylinders. Find the volume of cylinders in each case if the sheet measures 44 cm × 33 cm.
