The curved surface area of a cylinder is 1760cm^2 and its volume is 12320cm^3. Find radius
volume = pi r^2 h = 12320
area = 2 pi r h = 1760
so
h = 1760/2 pi r
and
12320 = pi r^2 (1760/2 pi r)
etc
v = pi r^2 h
a = 2pi r h
so, h = v/(pi r^2) = a/(2pi r)
r = 2v/a
To find the radius of the cylinder, we need to use the given information about its curved surface area and volume. Here's how you can solve for the radius of the cylinder:
Step 1: Find the height (h) of the cylinder:
The volume of a cylinder is given by the formula V = πr^2h, where V is the volume, r is the radius, and h is the height.
Given: V = 12320 cm^3
To find the height of the cylinder, we need to rearrange the formula for the volume:
h = V / (πr^2)
Step 2: Substitute the value of the height (h) in the formula for the curved surface area:
The curved surface area of a cylinder is given by the formula A = 2πrh, where A is the curved surface area, r is the radius, and h is the height.
Given: A = 1760 cm^2
Substitute the value of h from Step 1: A = 2πr(V / (πr^2))
Simplify the equation: 1760 = 2V / r
Step 3: Substitute the value of V and solve for r:
1760 = 2 * 12320 / r
1760 = 24640 / r
To eliminate the fraction, we can cross-multiply:
1760r = 24640
Step 4: Solve for r:
Divide both sides of the equation by 1760:
r = 24640 / 1760
r ≈ 14
Therefore, the radius of the cylinder is approximately 14 cm.