Advertisements
Advertisements
Question
The ratio of the radius and height of a cylinder is 2:3. If its volume is 12,936 cm3, find the total surface area of the cylinder.
Solution
The ratio of the radius and height of a cylinder = 2:3
Let the radius of the cylinder be 2x and the height of the cylinder be 3x.
Volume of the cylinder = 12936 cm3
∵ Volume of a cylinder = πr2h
∴ `12936 = 22/7 xx (2x)^3 xx 3x`
⇒ `12936 = 22/7 xx 4x^2 xx 3x`
⇒ `12936 = 264/7 x^3`
⇒ `x^3 = (12936 xx 7)/264 = 49 xx 7`
⇒ x3 = 7 × 7 × 7 = (7)3
⇒ x3 = (7)3
∴ x = 7
So, radius 2x = 2 × 7 = 14 cm and height = 3x = 3 × 7 = 21 cm
The total surface area of the cylinder = 2πr(r + h)
= `2 xx 22/7 xx 14(14 + 21)`
= `(44 xx 14)/7 xx 35`
= 44 × 14 × 5
= 3080 cm2
APPEARS IN
RELATED QUESTIONS
Curved surface area of a right circular cylinder is 4.4 m2. If the radius of the base of the cylinder is 0.7 m, find its height.
`["Assume "pi=22/7]`
The students of a Vidyalaya were asked to participate in a competition for making and decorating penholders in the shape of a cylinder with a base, using cardboard. Each penholder was to be of radius 3 cm and height 10.5 cm. The Vidyalaya was to supply the competitors with cardboard. If there were 35 competitors, how much cardboard was required to be bought for the competition?
`["Assume "pi=22/7]`
Find the height of the cylinder whose volume is 1.54 m3 and diameter of the base is 140 cm?
The diameter of roller 1.5 m long is 84 cm. If it takes 100 revolutions to level a playground, find the cost of levelling this ground at the rate of 50 paise per square metre.
A storage tank consists of a circular cylinder with a hemisphere adjoined on either end. If the
external diameter of the cylinder be 1.4 m and its length be 8 m, find the cost of painting it
on the outside at the rate of Rs. 10 per `m^2`.
Find the volume of a cylinder whose r = 3.5 cm, h = 40 cm .
A rectangular strip 25 cm × 7 cm is rotated about the longer side. Find the volume of the solid, thus generated.
A well with 10 m inside diameter is dug 8.4 m deep. Earth taken out of it is spread all around it to a width of 7.5 m to form an embankment. Find the height of the embankment.
Curved surface area of a cylinder is 1980 cm2 and radius of its base is 15 cm. Find the height of the cylinder. (π = `22/7`)
A cylindrical container with internal diameter of its base 20 cm, contains water upto a height of 14 cm. Find the area of the wet surface of the cylinder.
