The circumference of the base of a cylinder is 16 cm. The height of the cylinder is 10cm.
a. What is the surface area of the cylinder?
b. What is the volume of the cylinder?
Need help on this one. I have the formula but I'm a little confused because I don't know what the radius is. I think that if I have that then I will be able to just plug in the other numbers.
Circumference = PI * d
Solve for d and divide by 2.
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The circumference of the base of a cylinder is 16 π and the height is 21. Find the surface area of the cylinder.
To find the surface area and volume of a cylinder, you will need to know the radius. However, the given information only provides the circumference of the base and the height of the cylinder.
To determine the radius, you can use the formula for the circumference of a circle:
Circumference = 2πr
Given that the circumference of the base is 16 cm, you can plug this value into the formula and solve for the radius:
16 cm = 2πr
To isolate r, divide both sides of the equation by 2π:
r = 16 cm / (2π)
Now that you have determined the radius, you can proceed to find the surface area and volume of the cylinder.
a. Surface Area of the Cylinder: The formula for the surface area of a cylinder is given by:
Surface Area = 2πr(r + h)
Plug in the value of the radius found in the previous step (r) and the given height (h = 10 cm) into the formula:
Surface Area = 2π(16 cm / (2π))(16 cm / (2π) + 10 cm)
Simplify the expression by canceling out the common terms:
Surface Area = 2π(8 cm)(8 cm + 10 cm)
Calculate the values inside the brackets:
Surface Area = 2π(8 cm)(18 cm)
Multiply to find the surface area:
Surface Area = 288π cm² (rounded to the nearest whole number)
b. Volume of the Cylinder: The formula for the volume of a cylinder is given by:
Volume = πr²h
Plug in the value of the radius found earlier (r) and the given height (h = 10 cm) into the formula:
Volume = π(16 cm / (2π))²(10 cm)
Simplify the expression:
Volume = π(8 cm)²(10 cm)
Calculate the value inside the brackets:
Volume = π(64 cm²)(10 cm)
Multiply to find the volume:
Volume = 640π cm³ (rounded to the nearest whole number)
Therefore, the surface area of the cylinder is approximately 288π cm², and the volume of the cylinder is approximately 640π cm³.
The circumference is equal to (2)(pi)(r).
Since you know the circumference is 16,and you know the value of pi and 2,solve for r.