Question

exercises: find the volume of each cylinder below. show your work.
1.)
v = π·r²·h
= π·r·r·h
=
v = ______ cu. yd.
2.)
if you are given
the diameter,
you must divide
it by 2 in order to
find the radius.
v = ______ cu. in
3.)
h = 6 ft.
r = 9 ft.
v = ______ cu. ft.
4.)
5 yd
d = 14 yd
v = ______ cu. yd.
5.) find the volume of a cylinder with radius = 5½ yd. and height = 3 yd.
v = π·r·r·h
=
6.) find the volume of a cylinder with diameter of 18 ft. and height of 3 ft.

Explanation:

Step1: Calculate the volume of the first cylinder

For the first cylinder, \(r = 1\) yd and \(h=2\) yd. Using the formula \(V=\pi r^{2}h\), we substitute the values: \(V=\pi\times(1)^{2}\times2 = 2\pi\approx 2\times 3.14=6.28\) cu yd.

Step2: Calculate the volume of the second cylinder

For the second cylinder, the diameter \(d = 6\) in, so \(r=\frac{d}{2}=3\) in and \(h = 4\) in. Using \(V=\pi r^{2}h\), we substitute: \(V=\pi\times(3)^{2}\times4=\pi\times9\times 4 = 36\pi\approx36\times3.14 = 113.04\) cu in.

Step3: Calculate the volume of the third cylinder

For the third cylinder, \(r = 9\) ft and \(h = 6\) ft. Using \(V=\pi r^{2}h\), we substitute: \(V=\pi\times(9)^{2}\times6=\pi\times81\times6=486\pi\approx486\times3.14 = 1526.04\) cu ft.

Step4: Calculate the volume of the fourth cylinder

For the fourth cylinder, \(d = 14\) yd, so \(r=\frac{d}{2}=7\) yd and \(h = 5\) yd. Using \(V=\pi r^{2}h\), we substitute: \(V=\pi\times(7)^{2}\times5=\pi\times49\times5 = 245\pi\approx245\times3.14=769.3\) cu yd.

Step5: Calculate the volume of the fifth cylinder

For the fifth cylinder, \(r = 5.5\) yd and \(h = 3\) yd. Using \(V=\pi r^{2}h\), we substitute: \(V=\pi\times(5.5)^{2}\times3=\pi\times30.25\times3=90.75\pi\approx90.75\times3.14 = 285.955\) cu yd.

Step6: Calculate the volume of the sixth cylinder

For the sixth cylinder, \(d = 18\) ft, so \(r=\frac{d}{2}=9\) ft and \(h = 3\) ft. Using \(V=\pi r^{2}h\), we substitute: \(V=\pi\times(9)^{2}\times3=\pi\times81\times3=243\pi\approx243\times3.14 = 763.02\) cu ft.

Answer:

1. \(6.28\) cu yd
2. \(113.04\) cu in
3. \(1526.04\) cu ft
4. \(769.3\) cu yd
5. \(285.955\) cu yd
6. \(763.02\) cu ft