Advertisements
Advertisements
Question
The sum of the heights and the radius of a solid cylinder is 35 cm and its total surface area is 3080 cm2, find the volume of the cylinder.
Solution
Let r and h be the radius and height of a solid cylinder
Then, r + h = 35 cm
Total surface area of a cylinder = 3080 cm2
`=>` 2πr(h + r) = 3080
`=> 2 xx 22/7 xx r xx 35 = 3080`
`=>` 2 × 22 × r × 5 = 3080
`=> r = 3080/(2 xx 22 xx 5) = 14 cm`
`=>` h = 35 – r
= 35 – 14
= 21 cm
∴ Volume of cylinder = πr2h
= `22/7 xx 14 xx 14 xx 21`
= 12936 cm3
APPEARS IN
RELATED QUESTIONS
It costs Rs 2200 to paint the inner curved surface of a cylindrical vessel 10 m deep. If the cost of painting is at the rate of Rs 20 per m2, find
(i) Inner curved surface area of the vessel
(ii) Radius of the base
(iii) Capacity of the vessel
`["Assume "pi=22/7]`
From a solid right circular cylinder with height 10 cm and radius of the base 6 cm, a right circular cone of the same height and same base is removed. Find the volume of the remaining solid.
From a solid cylinder whose height is 16 cm and radius is 12 cm, a conical cavity of height 8 cm and of base radius 6 cm is hollowed out. Find the volume and total surface area of the remaining solid.
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 dimensions 7.5 m by 5 m by 4 m; calculate the rise in level in the cistern in 1 hour 15 minutes.
The height of a circular cylinder is 20 cm and the radius of its base is 7 cm. Find : the total surface area.
The total surface area of a hollow cylinder, which is open from both the sides, is 3575 cm2; area of its base ring is 357.5 cm2 and its height is 14 cm. Find the thickness of the cylinder.
A closed cylindrical tank, made of thin ironsheet, has diameter = 8.4 m and height 5.4 m. How much metal sheet, to the nearest m2, is used in making this tank, if `1/15` of the sheet actually used was wasted in making the tank?
If the circumference of a conical wooden piece is 484 cm then find its volume when its height is 105 cm.
The volume of a cylinder whose radius r is equal to its height is ______.
