Advertisements
Advertisements
प्रश्न
A vessel is in the form of hemispherical bowl surmounted by a hollow cylinder of same diameter. The diameter of the hemispherical bowl is 14 cm and the total height of the vessel is 13 cm. Find the total surface area of the vessel. `[\text{Use}pi=22/7]`
Advertisements
उत्तर
Let the radius and height of cylinder be r cm and h cm respectively.
Diameter of the hemispherical bowl = 14 cm
∴ Radius of the hemispherical bowl = Radius of the cylinder = r = `14/2` cm = 7 cm
Total height of the vessel = 13 cm
∴ Height of the cylinder, h = Total height of the vessel − Radius of the hemispherical bowl
= 13 cm − 7 cm = 6 cm
Total surface area of the vessel = 2 (curved surface area of the cylinder + curved surface area of the hemisphere) (Twice because the vessel is hollow)
`=2(2pirh+2pir^2)=4pir(h+r)=4xx22/7xx7xx(6+7)cm^2`
`=1144 cm^2`
Thus, the total surface area of the vessel is 1144 cm2.
APPEARS IN
संबंधित प्रश्न
A vessel is in the form of a hollow hemisphere mounted by a hollow cylinder. The diameter of the hemisphere is 14 cm and the total height of the vessel is 13 cm. Find the inner surface area of the vessel. [Use `pi = 22/7`]
From a solid right circular cylinder of height 2.4 cm and radius 0.7 cm, a right circular cone of same height and same radius is cut out. Find the total surface area of the remaining solid.
From a solid cylinder of height 7 cm and base diameter 12 cm, a conical cavity of same height and same base diameter is hollowed out. Find the total surface area of the remaining solid. [User `pi22/7`]
Find the volume of a solid in the form of a right circular cylinder with hemi-spherical ends whose total length is 2.7 m and the diameter of each hemi-spherical end is 0.7 m.
Two cubes each of volume 27 cm3 are joined end to end to form a solid. Find the surface area of the resulting cuboid.
The volume of a hemisphere is 2425 `1/2` cm3 . Find its curved surface area.
A rocket is in the form of a circular cylinder closed at the lower end and a cone of the same radius is attached to the top. The radius of the cylinder is 2.5 m, its height is 21 m and the slant height of the cone is 8 m. Calculate the total surface area of the rocket.
A copper wire of diameter 6 mm is evenly wrapped on a cylinder of length 18 cm and diameter 49 cm to cover its whole surface. Find the length and the volume of the wire. If the density of the copper be 8.8 g per cm3, then find the weight of the wire.
The total surface area of a solid hemisphere of radius 7 cm is ______.
Tamper-proof tetra-packed milk guarantees both freshness and security. This milk ensures uncompromised quality, preserving the nutritional values within and making it a reliable choice for health-conscious individuals.
500 ml milk is packed in a cuboidal container of dimensions 15 cm × 8 cm × 5 cm. These milk packets are then packed in cuboidal cartons of dimensions 30 cm × 32 cm × 15 cm.
Based on the above-given information, answer the following questions:
i. Find the volume of the cuboidal carton. (1)
ii. a. Find the total surface area of the milk packet. (2)
OR
b. How many milk packets can be filled in a carton? (2)
iii. How much milk can the cup (as shown in the figure) hold? (1)
