Bissoy.com
Doctors Medicines MCQs Q&A

Consider the following statements: 1. If the volume of a cylinder is 5π times the cube of its diameter, then the height of the cylinder is 20 times its radius. 2. If the curved surface area of a cylinder is 4π times the square of its diameter, then the height of the cylinder is 8 times its radius. Which of the above statements is/are correct?

Consider the following statements: 1. If the volume of a cylinder is 5π times the cube of its diameter, then the height of the cylinder is 20 times its radius. 2. If the curved surface area of a cylinder is 4π times the square of its diameter, then the height of the cylinder is 8 times its radius. Which of the above statements is/are correct? Correct Answer 2 only

Let the height and the radius of the cylinder be ‘h’ units and ‘r’ units respectively

Considering statement 1,

Volume of cylinder = 5π × (diameter)3

⇒ πr2h = 5π × (2r)3

⇒ πr2h = 5π × 8r3

⇒ h = 5 × 8r

⇒ h = 40r

Statement 1 is not correct

Considering statement 2,

Curved surface area of cylinder = 4π × (diameter)2

⇒ 2πrh = 4π × (2r)2

⇒ 2πrh = 4π × 4r2

⇒ h = 4 × 2r

⇒ h = 8r

Statement 2 is correct

∴ Only statement 2 is correct

Related Questions

“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 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?
Given below are three quantities named 1, 2 and 3. Based on the given information, you have to determine the relationship between the three quantities. You should use the given data and knowledge of Mathematics to choose between the possible answer. Quantity 1: Area of the innermost square. A square is made by joining the midpoints of a square of area 200 sq. m. The outermost square is called Square 1, The square inside it is called Square 2. The next square is made by joining midpoints of square 2 and is called Square 3. This process goes on. Square 5 is the innermost square. Quantity 2: A man starts with a speed of 10 km/hr. He increases his speed by 10 km/hr every hour at the start and drives at the same speed for that hour. If he traveled a total distance of 550 km. Find the time Quantity 3: Height of cylinder Its volume is equal to the volume of a cone whose radius is 14 cm and height is 39.3 cm. The radius of the cylinder is 14 cm
In this question two quantities are given. Find and compare them and choose the appropriate options. A cylinder of radius R and height H has the same volume as that of a sphere of radius r. The surface area of sphere is more than the curved surface area of cylinder. Quantity I: x, where 9x – 2 = 0 Quantity II: R/H; where a cylinder of radius R and height H has the same volume as that of a sphere of radius r. The surface area of sphere is more than the curved surface area of cylinder.
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.
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?
The curved surface area of cylinder X is 45% of the curved surface area of cylinder Y. If the volume of cylinder X is 27% of the volume of cylinder Y, then the height of cylinder X is what percentage of the height of cylinder Y?
Let X be a right circular cylinder with height ‘h’ and diameter ‘d’, Y be a right circular cone with height and diameter equal to that of cylinder X and Z be a sphere of maximum volume that can be inscribed in the cylinder X. Consider the following statements: 1. If d < h, then the volume of Y is (h/2d) times the volume of Z. 2. If d > h, then the volume of Y is (d2/2h2) times the volume of Z. Which of the above statements is/are correct?
The following question has three statements. Study the question and the statements and decide which of the statement(s) is necessary to answer the question. Find the height of the cylinder. I) The radius of the cylinder is equal to the side of the cube. II) The ratio of volumes of cylinder and cube is 2 ∶ 1. III) The cylinder has a curved surface area of 66 times its radius.
Which of the following statement(s) given below is / are TRUE? A: Volume of a cylinder with base area 38.5 cm2 and curved surface area 132 cm2 is 154 cm3. B: Total small spherical balls of radius 3 cm that can be casted after melting a large spherical ball of radius 15 cm is 25. C: Curved surface area of a cone of base radius 7 cm and height 24 cm is 540 cm2.