Advertisements
Advertisements
प्रश्न
The total surface area of a solid cylinder is 616 cm2. If the ratio between its curved surface area and total surface area is 1 : 2; find the volume of the cylinder.
उत्तर
Let r and h be the radius and height of a solid cylinder.
Total surface area of a cylinder = 616 cm2
`=>` 2πr(h + r) = 616
`=> pir(h + r) = 616/2`
`=>` πr(h + r) = 308 ...(i)
Curved surface area of a cylinder = 2πrh
Now, `"Curved surface area of a cylinder"/"Total surface area of a cylinder" = 1/2`
`=> (2pirh)/(2pir(h + r)) = 1/2`
`=> h/(h + r) = 1/2`
`=>` 2h = h + r
`=>` 2h – h = r
`=>` h = r
Substituting h = r in (i), we get
`=>` πr(r + r) = 308
`=>` πr.2r = 308
`=>` 2πr2 = 308
`=>` πr2 = 154
`=> 22/7 xx r^2 = 154`
`=> r^2 = (154 xx 7)/22`
`=>` r2 = 49
`=> r = sqrt(49)`
`=>` r = 7 cm
`=>` h = 7 cm.
∴ Volume of cylinder = πr2h
= `22/7 xx 7 xx 7 xx 7`
= 1078 cm3
APPEARS IN
संबंधित प्रश्न
Given a cylindrical tank, in which situation will you find surface area and in which situation volume.
- To find how much it can hold
- Number of cement bags required to plaster it
- To find the number of smaller tanks that can be filled with water from it.
A circus tent is cylindrical to a height of 8 m surmounted by a conical part. If total height of the tent is 13 m and the diameter of its base is 24 m; calculate :
- total surface area of the tent,
- area of canvas, required to make this tent allowing 10% of the canvas used for folds and stitching.
Water flows, at 9 km per hour, through a cylindrical pipe of cross-sectional area 25 cm2. If this water is collected into a rectangular cistern of imensions 7.5 m by 5 m by 4 m; calculate therise in level in the cistern in 1 hour 15 minutes.
Calculate:
(a) the total surface area,
(b) the total volume of the solid and
(c) the density of the material if its total weight is 1.7 kg..
A cylindrical vessel of height 24 cm and diameter 40 cm is full of water. Find the exact number of small cylindrical bottles, each of height 10 cm and diameter 8 cm, which can be filled with this water.
A metal container in the form of a cylinder is surmounted by a hemisphere of the same radius. The internal height of the cylinder is 7 m and the internal radius is 3.5 m. Calculate: the total area of the internal surface, excluding the base.
The radius of two right circular cylinder are in the ratio of 2 : 3 and their heights are in the ratio of 5: 4 calculate the ratio of their curved surface areas and also the ratio of their volumes.
Collect some old postcards. You can also use thick paper of size 14 cm x 9 cm.
Fold the postcard along the width to make pipe 1. Join the ends with cello tape.
Take another postcard and fold it along the length to make pipe 2. Join the ends with tape.
- Guess which pipe can take more sand inside it. Hold it on a plate and pour sand to check your guess. Was your guess correct? Discuss.
A cone, a hemisphere and a cylinder stand on equal bases and have the same height. The ratio of their volumes is 1 : 2 : 3.
If the radius of a cylinder is doubled and height is halved, the volume will be doubled.
A sphere and a right circular cylinder of the same radius have equal volumes. By what percentage does the diameter of the cylinder exceed its height?
