Advertisements
Advertisements
प्रश्न
A solid is composed of a cylinder with hemispherical ends. If the length of the whole solid is 108 cm and the diameter of the cylinder is 36 cm, find the cost of polishing the surface at the rate of 7 paise per cm2 .
उत्तर
Height of the cylinder = height of entire solid - height of sphere 1 - height of sphere 2
= 108 - 18 - 18
= 108 − 36
= 72 cm
r = 18 cm
C.S.A. of cylinder
\[= 2\pi r h\]
\[ = 2\pi \times 18 \times 72\]
\[ = 8138 . 88 {cm}^2\]
C.S.A. of 2 hemispheres = surface area of a sphere
\[= 4 \pi r^2 \]
\[ = 4\pi \left( 18 \right)^2 \]
\[ = 4069 . 44 {cm}^2\]
Surface area of solid
= 8138.88 + 4069.44
= 12208.32 cm2
Cost of polishing 1 cm2 = 7 paise = 0.07 Rs
Total cost
\[= 12208 . 32 \times 0 . 07\]
\[ = \text { Rs } 854 . 58\]
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`]
A tent is in the shape of a cylinder surmounted by a conical top. If the height and diameter of the cylindrical part are 2.1 m and 4 m respectively, and the slant height of the top is 2.8 m, find the area of the canvas used for making the tent. Also, find the cost of the canvas of the tent at the rate of Rs 500 per m2.
(Note that the base of the tent will not be covered with canvas.) [Use `pi = 22/7`]
Water in a canal, 5·4 m wide and 1·8 m deep, is flowing with a speed of 25 km/hour. How much area can it irrigate in 40 minutes, if 10 cm of standing water is required for irrigation?
A toy is in the form of a cone surmounted on a hemisphere. The diameter of the base and the height of cone are 6cm and 4cm. determine surface area of toy?
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.
A circus tent is cylindrical to a height of 4 m and conical above it. If its diameter is 105 m and its slant height is 40 m, the total area of the canvas required in m2 is
The total surface area of a solid hemisphere of radius r is ________.
Eight solid sphere of same size are made by melting a solid metallic cylinder of base diameter 6 cm and height 32 cm. The diameter of each sphere is ______.
A plumbline (sahul) is the combination of (see figure) ______.
