Advertisements
Advertisements
प्रश्न
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.
उत्तर
Radius of the cylinder = 3.5 m
Height = 7 m
Volume of the container = `pi"r"^2"h" + 2/3 pi "r"^3`
`=(22/7 xx 3.5 xx 3.5 xx 7)+(2/3 xx 22/7 xx 3.5 xx 3.5 xx3.5)`
`= 539/2 + 539/6`
`= (1617 + 539)/6`
`= 2156/6`
= 359.33 m3
संबंधित प्रश्न
A vessel is a hollow cylinder fitted with a hemispherical bottom of the same base. The depth of the cylindrical part is `4 2/3` m and the diameter of hemisphere is 3.5 m. Calculate the capacity and the internal surface area of the vessel.
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 has a diameter of 20 cm. The area of the curved surface is 100 cm2 (sq. cm). Find the volume of the cylinder correct to one decimal place.
The total surface area of a solid cylinder is 616 cm2. If the ratio between its curved surface area and total surface area is 1 : 2; find the volume of the cylinder.
Two right circular solid cylinders have radii in the ratio 3 : 5 and heights in the ratio 2 : 3. Find the ratio between their curved surface areas.
A glass cylinder with a diameter 20 cm water to a height of 9 cm. A metal cube of 8 cm edge is immersed in it completely. Calculate the height by which water will rise in the cylinder. (Take π = 3.142)
The diameter of the cross-section of a water pipe is 5 cm. Water flows through it at 10km/hr into a cistern in the form of a cylinder. If the radius of the base of the cistern is 2.5 m, find the height to which the water will rise in the cistern in 24 minutes.
A 14 m deep well with inner diameter 10 m is dug and the earth taken out is evenly spread all around the well to form an embankment of width 5 m. Find the height of the embankment.
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.
A solid metallic cylinder is cut into two identical halves along its height (as shown in the diagram). The diameter of the cylinder is 7 cm and the height is 10 cm.
Find:
- The total surface area (both the halves).
- The total cost of painting the two halves at the rate of ₹ 30 per cm2 `("Use" π = 22/7)`.
