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
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 Rs. 5 per 100 sq. cm. [Use π = 3.14]
In Fig. 5, is a decorative block, made up two solids – a cube and a hemisphere. The base of the block is a cube of side 6 cm and the hemisphere fixed on the top has diameter of 3.5 cm. Find the total surface area of the bock `(Use pi=22/7)`
A solid wooden toy is in the form of a hemisphere surrounded by a cone of same radius. The radius of hemisphere is 3.5 cm and the total wood used in the making of toy is 166 `5/6` cm3. Find the height of the toy. Also, find the cost of painting the hemispherical part of the toy at the rate of Rs 10 per cm2 .[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 tent of height 77dm is in the form a right circular cylinder of diameter 36m and height 44dm surmounted by a right circular cone. Find the cost of canvas at Rs.3.50 per m2 ?
A bucket made of aluminum sheet is of height 20cm and its upper and lower ends are of radius 25cm an 10cm, find cost of making bucket if the aluminum sheet costs Rs 70 per
100 cm2
How many spherical lead shots each of diameter 4.2 cm can be obtained from a solid rectangular lead piece with dimension 6cm \[\times\] 42cm \[\times\] 21 cm.
A solid cuboid of iron with dimensions 53 cm ⨯ 40 cm ⨯ 15 cm is melted and recast into a cylindrical pipe. The outer and inner diameters of pipe are 8 cm and 7 cm respectively. Find the length of pipe.
The inner and outer radii of a hollow cylinder are 15 cm and 20 cm, respectively. The cylinder is melted and recast into a solid cylinder of the same height. Find the radius of the base of new cylinder.
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.
A solid metal sphere of 6 cm diameter is melted and a circular sheet of thickness 1 cm is prepared. Determine the diameter of the sheet.
The volume of a hemisphere is 2425 `1/2` cm3 . Find its curved surface area.
A right triangle whose sides are 15 cm and 20 cm (other than hypotenuse), is made to revolve about its hypotenuse. Find the volume and surface area of the double cone so formed. (Choose value of π as found appropriate)
Five identical cubes, each of edge 5 cm, are placed adjacent to each other. Find the volume of the resulting cuboid.
If the areas of three adjacent faces of a cuboid are x, y and z, respectively, the volume of the cuboid 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 ______.
If two solid hemispheres of same base radius r are joined together along their bases, then curved surface area of this new solid is ______.
A solid cone of radius r and height h is placed over a solid cylinder having same base radius and height as that of a cone. The total surface area of the combined solid is `pir [sqrt(r^2 + h^2) + 3r + 2h]`.
