Advertisements
Advertisements
प्रश्न
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)`
Advertisements
उत्तर
Let the radius of base and height of the solid right circular cylinder be r cm and h cm, respectively.
According to the question,
r+h=37 .....(1)
Total surface area=1628 sq cm
2πr(r+h)=1628 .....(2)
From (1) and (2), we get
2πr(37)=1628
⇒ 2πr=44
`=>2xx22/7xxr=44`
`=>r=(44xx7)/(2xx22)`
⇒ r = 7 cm
Substituting the value of r in (1), we get
7+h=37
⇒ h = 30 cm
Now,
Volume of the cylinder = πr2h
`=22/7xx7xx7xx30`
=4,620 cm3
Hence, the volume of the cylinder is 4,620 cm3.
संबंधित प्रश्न
In Fig. 5, from a cuboidal solid metallic block, of dimensions 15cm ✕ 10cm ✕ 5cm, a cylindrical hole of diameter 7 cm is drilled out. Find the surface area of the remaining block [Use
`pi=22/7`]
From a solid cylinder whose height is 2.4 cm and diameter 1.4 cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid to the nearest cm2
[use `pi = 22/7`]
A wooden article was made by scooping out a hemisphere from each end of a solid cylinder, as shown in given figure. If the height of the cylinder is 10 cm, and its base is of radius 3.5 cm, find the total surface area of the article.
[Use `pi = 22/7`]
The radii of the circular bases of a frustum of a right circular cone are 12 cm and 3 cm and the height is 12 cm. Find the total surface area and the volume of the frustum.
If the radius of the base of a right circular cylinder is halved, keeping the height the same, then the ratio of the volume of the cylinder thus obtained to the volume of original cylinder is:
Find the number of metallic circular discs with a 1.5 cm base diameter and of height 0.2 cm to be melted to form a right circular cylinder of height 10 cm and diameter 4.5 cm.
The largest cone is curved out from one face of solid cube of side 21 cm. Find the volume of the remaining solid.
Three solid spheres of radii 3, 4 and 5 cm respectively are melted and converted into a single solid sphere. Find the radius of this sphere.
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 cubical block of side 10 cm is surmounted by a hemisphere. What is the largest diameter that the hemisphere can have? Find the cost of painting the total surface area of the solid so formed, at the rate of ₹5 per 100 sq cm. [Use ππ = 3.14]
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.
Find the ratio of the volume of a cube to that of a sphere which will fit inside it.
A plumbline (sahul) is a combination of
The volume of a hemisphere is 19404 cm3. The total surface area of the hemisphere is
If the surface areas of two spheres are in ratio 16 : 9, then their volumes will be in the ratio ______.
If the volumes of a cube is 1728 cm³, the length of its edge is equal to ______.
The curved surface area of glass having radii 3 cm and 4 cm respectively and slant height 10 cm is ______.
The shape of a gilli, in the gilli-danda game (see figure), is a combination of ______.
|
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?
