Advertisements
Advertisements
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.
उत्तर
Diameter of the base = 3.5 m
Therefore, radius =`3.5/2 m = 1.75 m = 7/4 m`
Height of cylindrical part = `4 2/3 = 14/3 m `
(i) Capacity (volume) of the vessel
= `pir^2h + 2/3pir^3`
= `pir^2(h + 2/3r)`
= `22/7 xx 7/4 xx 7/4(14/3 + 2/3 xx 7/4)`
= `77/8(14/3 + 7/6)`
= `77/8((28 + 7)/6)`
= `77/8 xx 35/6`
= `2695/48`
= 56.15 m3
(ii) Internal curved surface area
= `2pirh + 2pir^2 = 2pir(h + r) `
= `2 xx 22/7 xx 7/4(14/3 + 7/4)`
= `11((56 + 21)/12)`
= `11 xx 77/12`
= `847/12`
= 70.58 m2
APPEARS IN
संबंधित प्रश्न
The inner diameter of a cylindrical wooden pipe is 24 cm and its outer diameter is 28 cm. The length of the pipe is 35 cm. Find the mass of the pipe, if 1 cm3 of wood has a mass of 0.6 g.
`["Assume "pi=22/7]`
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.
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.
3080 cm3 of water is required to fill a cylindrical vessel completely and 2310 cm3 of water is required to fill it upto 5 cm below the top. Find :
- radius of the vessel.
- height of the vessel.
- wetted surface area of the vessel when it is half-filled with water.
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-cylinder have bases of the same size. The diameter of each is 14 cm. One of the cones is 10 cm high and the other is 20 cm high. Find the ratio between their volumes.
If the circumference of a conical wooden piece is 484 cm then find its volume when its height is 105 cm.
Volume of a cylinder with radius h and height r is ______.
The thickness of a hollow metallic cylinder is 2 cm. It is 70 cm long with outer radius of 14 cm. Find the volume of the metal used in making the cylinder, assuming that it is open at both the ends. Also find its weight if the metal weighs 8 g per cm3.
A hollow garden roller of 42 cm diameter and length 152 cm is made of cast iron 2 cm thick. Find the volume of iron used in the roller.
