The Curved surface area of the cylinder is 1760cm^2 .and its volume is 12320 cm^3. Find its height
2πrh = 1760
πr^2h = 12320
square the area equation, and now you have
4π^2 r^2 h^2 = 1760^2
πr^2 h = 12320
Divide and you have
4πh = 1760^2/12320
...
To find the height of the cylinder, we can use the formula for the curved surface area and volume of a cylinder.
The formula for the curved surface area of a cylinder is given by:
CSA = 2πrh, where CSA is the curved surface area, π is a constant approximately equal to 3.14, r is the radius of the base, and h is the height of the cylinder.
The formula for the volume of a cylinder is given by:
V = πr^2h, where V is the volume, π is a constant approximately equal to 3.14, r is the radius of the base, and h is the height of the cylinder.
Given that the curved surface area of the cylinder is 1760 cm^2 and the volume is 12320 cm^3, we can set up two equations:
Equation 1: CSA = 2πrh, where CSA = 1760 cm^2
Equation 2: V = πr^2h, where V = 12320 cm^3
Now we can solve these equations simultaneously to find the height of the cylinder.
Step 1: Substitute the value of CSA in Equation 1:
1760 = 2πrh
Step 2: Solve Equation 1 for r in terms of h:
r = 1760 / (2πh)
Step 3: Substitute the value of r from Step 2 into Equation 2:
12320 = π(1760 / (2πh))^2 * h
Step 4: Simplify Equation 3:
12320 = (1760^2 / 4π) * h
Step 5: Solve for h:
h = (12320 * 4π) / 1760^2
Step 6: Calculate the value of h:
h ≈ 4.5 cm
Therefore, the height of the cylinder is approximately 4.5 cm.