Bissoy.com
Doctors Medicines MCQs Q&A

The ratio of the curved surface area of a right circular cylinder to the total area of its bases is 3 : 2. if the total surface area of the cylinder is 308000 cm3, then what is the volume of the cylinder?

The ratio of the curved surface area of a right circular cylinder to the total area of its bases is 3 : 2. if the total surface area of the cylinder is 308000 cm3, then what is the volume of the cylinder? Correct Answer 1,29,36,000 cm<sup>3</sup>

Given:

The ratio of curved surface area of cylinder ant total area of its bases is 3 : 2

total surface area of cylinder = 308000 cm3

Concept used:

Curved surface area of cylinder = 2πrh

Total surface area of cylinder = 2πr(r + h)

Area of base of cylinder = πr2

Volume of cylinder = πr2h

Calculation:

in cylinder its bases is 2

2πrh : 2πr2 = 3 : 2

⇒ h : r = 3 : 2

∵ 2πr(r + h) = 308000

⇒ 2π × 2x(2x + 3x) = 308000

⇒ 2π × 10x2 = 308000

⇒ (22/7) × x2 = 15400

⇒ x2 = 4900

⇒ x = 70

now,

Volume = π × (2x)2 × 3x

⇒ Volume = π × 12x3

⇒ Volume = 22/7 × (12 × 703)

⇒ Volume = 22 × 12 × 70 × 70 × 10

∴ Volume = 1,29,36,000 cm3

Related Questions

Which of the following statements is/are true? A: If radius of a cylinder is decreased by 50% and its volume remains same, then its height will be increased by 200%. B: Difference between the curved surface area and total surface area of a cone is equal to the area of its circular base. C: If height of a cylinder is equal to its radius, then its curved surface area will be equal to the total area of its both the circular bases.
“What is the different between height and radius of solid cylinder?” Which of the following option is sufficient alone to find the answer? A) A solid cylinder is made by melting a solid sphere. The radius of cylinder is 3 times the radius of a circle whose area is 154 sq.m. Height of cylinder is equal to the height of cone whose volume is 2772 cubic meters. B) Area of a rectangle whose longer side is ¾ times the radius of a solid cylinder, is 168 sq.m and, Volume of solid cylinder is 2772 cubic meters and its height is 18 m. C) A metallic cone of radius 15m and height 35m is melted into the solid cylinder of radius equal to the radius of a circle whose area is equal to the area of rectangle whose sides are in the ratio 4 : 3 respectively. D) The curved surface area of the solid cylinder is 3 time the surface area of a sphere of radius 7m and height of cylinder is equal to the height of a metallic cone whose curved surface area is 308 sq.m. 
A right circular cylinder is formed. A = Sum of total surface area and the area of the two bases. B = Curved surface area of this cylinder. If A ∶ B = 3 ∶ 2 and the volume of cylinder is 4312 cm3, then what is the sum of area (in cm2) of the two bases of this cylinder?
A right circular cylinder is formed. A = sum of total surface area and the area of the two bases. B = the curved surface area of this cylinder. If A : B = 3 : 2 and the volume of cylinder is 4312 cm3, then what is the sum of area (in cm2) of the two bases of this cylinder?
The ratio of curved surface area of a right circular cylinder to the total area of its two bases is 2 : 1. If the total surface area of cylinder is 23100 cm2, then what is the volume (in cm3) of cylinder?
The ratio of curved surface area of a right circular cylinder to the total area of its two bases is 2 : 1. If the total surface area of cylinder is 23100 cm2,then what is the volume (in cm3) of cylinder?
A cube is inscribed in a sphere. A right circular cylinder is within the cube touching all the vertical faces. A right circular once is inside the cylinder. Their heights are same and the diameter of the cone is equal to that of the cylinder. Consider the following statements: 1) The surface area of the sphere is √5 Times the curved surface area of the cone. 2) The surface area of the cube is equal to the curved surface area of the cylinder. Which of the above statements is/are correct?
The ratio of the curved surface area and total surface area of a right circular cylinder is 2 : 5. If the total surface area is 3080 cm2, then what is the volume (in cm3) of the cylinder?
The ratio of the curved surface area and total surface area of a right circular cylinder is 2 : 5. If the total surface area is 3080 cm2, then what is the volume(in cm3) of the cylinder?
The curved surface area of cylinder A is 8% more than the curved surface area of cylinder B. If the height of cylinder A is 4% less than the height of cylinder B, then the volume of cylinder A is what percentage more/less than the volume of cylinder B?