Find the volume and surface area of a right cylinder with radius 7.5 cm and height 16 in. Make sure your final answer is in inches. Round your answer to the nearest hundredth.
v = pi r^2 h
= 3.1416 * 7.5^2 * 16
= 1827.44 in^3
a = 2pi*r(r+h)
= 2*3.1416*7.5(7.5+16)
= 1107.41 in^2
Thanks, Steve. I believe we were supposed to convert the 16 inches into centimeters first (which is 40.64 cm, right?) to solve for both V and A and then take our final, not-rounded answer, convert it back into inches, and then round.
oops - you are correct. I didn't watch the units!
6cm and height h=16cm round it off yor answer to the nearest =3.14
To find the volume and surface area of a right cylinder, we will use the following formulas:
Volume of a cylinder = π * r^2 * h
Surface area of a cylinder = 2 * π * r^2 + 2 * π * r * h
Given that the radius (r) of the cylinder is 7.5 cm and the height (h) is 16 in, we need to convert the radius from centimeters to inches to ensure consistent units in our final answer.
To convert cm to inches, we use the conversion factor: 1 inch = 2.54 cm.
Converting the radius:
Radius in inches (r_inch) = 7.5 cm / 2.54 cm/inch = 2.95 inches (rounded to the nearest hundredth)
Now that we have the radius in inches, we can calculate the volume and surface area of the cylinder.
Volume of the cylinder:
Volume = π * r^2 * h
Volume = π * (2.95 inches)^2 * 16 inches
Volume ≈ 139.21 cubic inches (rounded to the nearest hundredth)
Surface area of the cylinder:
Surface area = 2 * π * r^2 + 2 * π * r * h
Surface area = 2 * π * (2.95 inches)^2 + 2 * π * 2.95 inches * 16 inches
Surface area ≈ 329.07 square inches (rounded to the nearest hundredth)
Therefore, the volume of the cylinder is approximately 139.21 cubic inches, and the surface area is approximately 329.07 square inches.