The radius of a cylinder is 3.5 ft. The height is 14 ft. Find the surface area and volume of the cylinder to the nearest tenth of a foot. SHOW YOUR WORK!
a = 2πr(r+h)
v = 1/3 πr^2 h
Since v is directly proportional to r^2, reducing r by 1/3 will reduce v by 1/9:
π(1/3 r)^2 h = π(1/9 r^2)h = 1/9 πr^2h = 1/9 v
To find the surface area of a cylinder, we need to calculate the area of the two bases and the lateral surface area.
The formula for the area of a circle is:
A = πr^2
where A is the area and r is the radius.
Given that the radius of the cylinder is 3.5 ft, and using π (pi) as approximately 3.14159, we can calculate the area of each base:
Base Area = π(3.5)^2
Now let's calculate the lateral surface area. The lateral surface area is the area of the curved surface of the cylinder.
The formula for the lateral surface area of a cylinder is:
Lateral Surface Area = 2πrh
where r is the radius and h is the height.
Given that the radius is 3.5 ft and the height is 14 ft, we can calculate the lateral surface area:
Lateral Surface Area = 2π(3.5)(14)
Finally, to find the total surface area, we need to add the two base areas to the lateral surface area:
Total Surface Area = 2(Base Area) + Lateral Surface Area
Now, let's calculate the volume of the cylinder.
The formula for the volume of a cylinder is:
Volume = Base Area * height
Given that the radius is 3.5 ft, the height is 14 ft, and using the same value of π, we can calculate the volume of the cylinder:
Volume = Base Area * 14
To find the answer, let's plug in the values and do the calculations:
Base Area = 3.14159 * (3.5)^2
Lateral Surface Area = 2 * 3.14159 * 3.5 * 14
Total Surface Area = 2 * (Base Area) + Lateral Surface Area
Volume = (Base Area) * 14
After evaluating these calculations, the surface area of the cylinder is approximately _______ square feet (nearest tenth of a foot), and the volume of the cylinder is approximately _______ cubic feet (nearest tenth of a foot).