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
The largest possible sphere is carved out of a wooden solid cube of side 7 em. Find the volume of the wood left. (Use\[\pi = \frac{22}{7}\]).
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.
The diameters of the lower and upper ends of a bucket in the form of a frustum of a cone are 10 cm and 30 cm respectively. If its height is 24 cm, find:
1) The area of the metal sheet used to make the bucket.
2) Why we should avoid the bucket made by ordinary plastic? [Use π = 3.14]
A metallic cylinder has radius 3 cm and height 5 cm. To reduce its weight, a conical hole is drilled in the cylinder. The conical hole has a radius of `3/2` cm and its depth is `8/9 `cm. Calculate the ratio of the volume of metal left in the cylinder to the volume of metal taken out in conical shape.
The volume of a hemisphere is 2425 `1/2` cm3 . Find its curved surface area.
From a solid cylinder of height 2.8 cm and diameter 4.2 cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid.
A hemispherical bowl of internal diameter 30 cm contains some liquid. This liquid is to be poured into cylindrical bottles of diameter 5 cm and height 6 cm each. Find the number of bottles required.
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.
Five identical cubes, each of edge 5 cm, are placed adjacent to each other. Find the volume of the resulting cuboid.
Two cubes each of volume 8 cm³ are joined end to end, then the surface area of the resulting cuboid is ______.
