QQuestion
The height of a right circular cylinder is twice the radius of the base. If the height is 6 times of the radius, then the volume of the cylinder is 539 cubic decimeter more than the previous volume. Find the height of the cylinder.
✓Answer
Let the original radius of the base be r and the original height be h.
From the given condition:
h = 2r
The volume of a cylinder is given by:
V = π r² h
Substituting h = 2r in the volume formula:
V₁ = π r² (2r)
V₁ = 2π r³
Now, the new height is 6 times the radius, so:
h’ = 6r
The new volume is:
V₂ = π r² (6r)
V₂ = 6π r³
According to the problem, the difference in volume is 539 cubic decimeters:
V₂ – V₁ = 539
Substituting the values of V₁ and V₂:
6π r³ – 2π r³ = 539
4π r³ = 539
Substituting π ≈ \frac{22}{7} :
4 × \frac{22}{7} × r³ = 539
\frac{88}{7} × r³ = 539
Multiplying both sides by 7:
88 r³ = 3773
⇒ r³ = \frac{3773}{88}
⇒ r³ = \frac{343}{8}
⇒ r = 3.5 dm
∴ height = 2r
= 2 × 3.5
= 7 cm
Related Questions
More WBBSE Moderate level questions
The ratio of the length of radius of two solid right circular cylinders is 2:3 and the ratio of their heights is 5:3. Find the ratio of the area of curved surfaces.
Difference of outer and inner curved surface area of a hollow cylindrical pipe is 44 sq.cm and length is 14 cm. If the Volume of the material of the pipe be 99 cubic cm. Find inner and outer radius.
The curved surface area of a right circular cylindrical wooden log of uniform density is 440 sq. decimeters. The weight of 1 cubic decimeter of wood is 3 kg and the weight of a log is 18.48 quintals. Find the diameter of the log.
The height of a right circular cylinder is twice its radius. If the height would be 6 times its radius, then the volume of the cylinder would be greater by 539 cubic dm. Calculate the height of the cylinder.
If the height of two right circular cylinders is in the ratio of 1 : 2, and the perimeters of the base are in the ratio of 3 : 4, find the ratio of their volumes.
Draw an ogive on the graph paper after calculating the cumulative frequency (less than type) of the following data: Class Interval Frequency 0 - 10 1 10 - 20 5 20 - 30 15 30 - 40 20 40 - 50 15 50 - 60 6 60 - 70 1
The median of following data is 32. Find the value of x and y if x + y = 100. Class Interval Frequency 0 - 10 10 10 - 20 x 20 - 30 25 30 - 40 30 40 - 50 y 50 - 60 10
Melting a solid Lead sphere of diameter 12 cm, three small solid spheres are made. If the ratio of the diameter of the small spheres is 3 : 4 : 5 then find the radius of each small sphere
Curved surface area of a right circular cone is 154√2 sq cm and radius of the base 7 cm. Find its vertical angle.
Find the ratio of length of radius and perimeter of a circle
If the roots of a quadratic equation ax² + bx + c = 0 (a ≠ 0) are reciprocal and opposite in sign. Find (a + c)
Find x, if sin x = cos (x – 20°)