Advertisements
Advertisements
Question
The radius of the base and the height of a solid right circular cylinder are in the ratio 2 : 3 and its volume is 1617 cm3. Find the total surface area of the cylinder.
Solution
Let the radius of the cylinder be 2x cm and its height be 3x cm.
Then,Volume of the cylinder`=pi"r"^2"h"`
`=22/7xx(2x)^2xx3x`
Therefore,
`22/7xx(2x)^2xx3x=1617`
`=>22/7xx4x^2xx3x=1617`
`=> 22/7xx12x^3 = 1617`
`=>x^3=(1617+7/22xx12)`
`=> x^3=(7/2xx7/2xx7/2)`
`=> x^3 = (7/2)^3`
`=> x = 7/2`
Now, r = 7 cm and `"h" = 21/2 "cm"`
Hence,the total surface area of the cylinder:
(2πrh + 2πr2)
= 2πr(h + r)
`= 2xx22/7xx7xx(21/2+7)"cm"^`
`= (2xx(22)/7xx7xx(35)/2) "cm"^2 `
= 770 cm2
APPEARS IN
RELATED QUESTIONS
Sushant has a vessel, of the form of an inverted cone, open at the top, of height 11 cm and radius of top as 2.5 cm and is full of water. Metallic spherical balls each of diameter 0.5 cm are put in the vessel due to which 2/5 th of the water in the vessel flows out. Find how many balls were put in the vessel. Sushant made the arrangement so that the water that flows out irrigates the flower beds. What value has been shown by Sushant?
A copper wire, 3 mm in diameter, is wound about a cylinder whose length is 12 cm, and diameter 10 cm, so as to cover the curved surface of the cylinder. Find the length and mass of the wire, assuming the density of copper to be 8.88 g per cm3.
An iron pillar consists of a cylindrical portion 2.8 m high and 20 cm in diameter and a cone 42 cm high is surmounting it. Find the weight of the pillar, given that 1 cubic cm of iron weighs 7.5 gm.
What is the ratio of the volumes of a cylinder, a cone and a sphere, if each has the same diameter and same height?
A cylinder, a cone and a hemisphere are of equal base and have the same height. What is the ratio of their volumes?
Choose the correct answer of the following question:
The surface areas of two spheres are in the ratio 16 : 9. The ratio of their volumes is
The length of the longest pole that can be kept in a room (12 m × 9 m ×8 m) is
The volume of a cube is 2744 cm2. Its surface area is
Assertion (A)
The outer surface of a hemisphere of radius 7 cm is to be painted. The total cost of painting at Rs 5 per cm2 is Rs 2300.
Reason (R)
The total surface area of a hemisphere is 3π r2.
- Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).
- Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).
- Assertion (A) is true and Reason (R) is false.
- Assertion (A) is false and Reason (R) is true.
The internal and external radii of a spherical shell are 3cm and 5cm respectively. It is melted and recast into a solid cylinder of diameter 14 cm, find the height of the cylinder. Also find the total surface area of the cylinder. (Take `pi = 22/7`)
