how to find the radius of a cylinder given the volume and height
The volume of a cylinder is the density of the cylinder which signifies the amount of material it can carry or how much corporeality of any cloth can be immersed in it. Cylinder's volume is given past the formula,πr2h, where r is the radius of the circular base and h is the height of the cylinder. The material could be a liquid quantity or any substance which can exist filled in the cylinder uniformly. Check book of shapes here.
Volume of cylinder has been explained in this article briefly along with solved examples for better understanding. In Mathematics, geometry is an of import branch where we learn the shapes and their properties. Volume and area are the two important properties of any 3d shape.
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Definition
The cylinder is a three-dimensional shape having a circular base. A cylinder can be seen as a set up of circular disks that are stacked on ane another. Now, think of a scenario where we need to calculate the amount of sugar that can exist accommodated in a cylindrical box.
In other words, nosotros mean to calculate the capacity or volume of this box. The capacity of a cylindrical box is basically equal to the book of the cylinder involved. Thus, the volume of a three-dimensional shape is equal to the amount of space occupied past that shape.
Volume of a Cylinder Formula
A cylinder can be seen every bit a collection of multiple congruent disks, stacked one higher up the other. In gild to calculate the infinite occupied past a cylinder, we calculate the infinite occupied by each disk and then add them upwardly. Thus, the volume of the cylinder tin be given by the production of the surface area of base and top.
For whatever cylinder with base of operations radius 'r', and meridian 'h', the volume volition be base times the superlative.
Therefore, the cylinder's book of base radius 'r', and acme 'h' = (expanse of base) × meridian of the cylinder
Since the base is the circle, it tin can be written equally
Volume = πrii× h
Therefore, the volume of a cylinder = πr2h cubic units.
Volume of Hollow Cylinder
In case of hollow cylinder, we measure two radius, one for inner circle and one for outer circle formed past the base of hollow cylinder. Suppose, ri and r2 are the 2 radii of the given hollow cylinder with 'h' equally the height, then the volume of this cylinder can be written as;
- Five = πh(ri ii – r2 two)
Surface Area of Cylinder
The amount of square units required to cover the surface of the cylinder is the surface area of the cylinder. The formula for the area of the cylinder is equal to the total surface area of the bases of the cylinder and surface surface area of its sides.
- A = 2πr2 + 2πrh
Volume of Cylinder in Litres
When we find the volume of the cylinder in cubic centimetres, we tin convert the value in litres by knowing the beneath conversion, i.e.,
1 Litre = 1000 cubic cm or cm3
For example: If a cylindrical tube has a book of 12 litres, then nosotros tin write the volume of the tube as 12 × grand cmiii = 12,000 cm3
Examples
Question 1: Summate the volume of a given cylinder having top twenty cm and base of operations radius of 14 cm. (Take pi = 22/vii)
Solution:
Given:
Tiptop = 20 cm
radius = xiv cm
we know that;
Volume, V = πrtwoh cubic units
5=(22/7) × 14 × 14 × 20
V= 12320 cmthree
Therefore, the volume of a cylinder = 12320 cmiii
Question 2: Summate the radius of the base of a cylindrical container of volume 440 cmiii. Height of the cylindrical container is 35 cm. (Take pi = 22/vii)
Solution:
Given:
Volume = 440 cm3
Superlative = 35 cm
We know from the formula of cylinder;
Volume, V = πr2h cubic units
Then, 440 =(22/7) × r2 × 35
r2= (440× vii)/(22 × 35) = 3080/770 = 4
Therefore, r = 2 cm
Therefore, the radius of a cylinder = ii cm.
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