Advertisements
Advertisements
प्रश्न
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?
Advertisements
उत्तर
Given height of cone (h) = 4cm
Diameter of cone (d) = 6cm
∴Radius (r) =`6/2 =3 cm`
Let ‘l’ be slant height of cone
`l=sqrt(r^2+h^2)`
`=sqrt(3^2+4^2) =5cm`
l = 5cm
∴ Slant height of cone (l) = 5cm.
Curved surface area of cone (S1) = πrl
S1 = π(3)(5) = 47.1cm2
Curved surface area of hemisphere (S2) = 2πr2
`S_2=2pi(3)^2=56.52cm^2`
∴Total surface area(S) = S1 + S2
= 47.1 + 56.52
= 103.62cm2
∴ Curved surface area of toy = 103.62cm2
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\[\pi = \frac{22}{7}\]).
Water in a canal, 6 m wide and 1.5 m deep, is flowing at a speed of 4 km/h. How much area will it irrigate in 10 minutes, if 8 cm of standing water is needed for irrigation?
The sum of the radius of base and height of a solid right circular cylinder is 37 cm. If the total surface area of the solid cylinder is 1628 sq. cm, find the volume of the cylinder. `("use " pi=22/7)`
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 [take π=22/7]
A medicine capsule is in the shape of cylinder with two hemispheres stuck to each of its ends (see the given figure). The length of the entire capsule is 14 mm and the diameter of the capsule is 5 mm. Find its surface area. [Use π = `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.
Prove that the surface area of a sphere is equal to the curved surface area of the circumference cylinder__?
A cylindrical tub, whose diameter is 12 cm and height 15 cm is full of ice-cream. The whole ice-cream is to be divided into 10 children in equal ice-cream cones, with conical base surmounted by hemispherical top. If the height of conical portion is twice the diameter of base, find the diameter of conical part of ice-cream cone ?
Two cubes each of volume 27 cm3 are joined end to end to form a solid. Find the surface area of the resulting cuboid.
A cylindrical bucket 28 cm in diameter and 72 cm high is full of water. The water is emptied into a rectangular tank 66 cm long and 28 cm wide. Find the height of the water level in the tank.
Volume and surface area of a solid hemisphere are numerically equal. What is the diameter of hemisphere?
The shape of the gilli used in a gilli-danda game is a combination of
A cone of height 24 cm and radius of base 6 cm is made up of modelling clay. A child reshapes it in the form of a sphere. Find the radius of the sphere and hence find the surface area of this sphere.
The radius of spherical balloon increases from 8 cm to 12 cm. The ratio of the surface areas of balloon in two cases 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 ______.
The curved surface area of glass having radii 3 cm and 4 cm respectively and slant height 10 cm is ______.
|
Khurja is a city in the Indian state of Uttar Pradesh famous for the pottery. Khurja pottery is traditional Indian pottery work which has attracted Indians as well as foreigners with a variety of tea sets, crockery and ceramic tile works. A huge portion of the ceramics used in the country is supplied by Khurja and is also referred as "The Ceramic Town". One of the private schools of Bulandshahr organised an Educational Tour for class 10 students to Khurja. Students were very excited about the trip. Following are the few pottery objects of Khurja.
Students found the shapes of the objects very interesting and they could easily relate them with mathematical shapes viz sphere, hemisphere, cylinder etc. |
Maths teacher who was accompanying the students asked the following questions:
- The internal radius of hemispherical bowl (filled completely with water) in I is 9 cm and the radius and height of the cylindrical jar in II are 1.5 cm and 4 cm respectively. If the hemispherical bowl is to be emptied in cylindrical jars, then how many cylindrical jars are required?
- If in the cylindrical jar full of water, a conical funnel of the same height and same diameter is immersed, then how much water will flow out of the jar?
The boilers are used in thermal power plants to store water and then used to produce steam. One such boiler consists of a cylindrical part in middle and two hemispherical parts at its both ends.
Length of the cylindrical part is 7 m and radius of cylindrical part is `7/2` m.
Find the total surface area and the volume of the boiler. Also, find the ratio of the volume of cylindrical part to the volume of one hemispherical part.
Statement A (Assertion): Total Surface area of the top is the sum of the curved surface area of the hemisphere and the curved surface area of the cone.
Statement R( Reason): Top is obtained by joining the plane surfaces of the hemisphere and cone together.
