Question

copy and solve for exercises 10 - 27, show your work and answers on a separate piece of paper. find the volume of each cylinder. round to the nearest tenth. 10. 12. 13. kyle has a container of flour in the

Explanation:

Step1: Recall the formula for the volume of a cylinder

The formula for the volume of a cylinder is \(V=\pi r^{2}h\), where \(r\) is the radius and \(h\) is the height.

Step2: Find the radius for the first cylinder (Exercise 10)

Given the diameter \(d = 24\space mm\), the radius \(r=\frac{d}{2}=\frac{24}{2}=12\space mm\), and \(h = 5\space mm\).
Substitute into the formula: \(V=\pi\times(12)^{2}\times5=\pi\times144\times5 = 720\pi\space mm^{3}\approx720\times3.14 = 2260.8\space mm^{3}\)

Step3: Find the radius for the second cylinder (Exercise 11)

Given the diameter \(d = 21\space yd\), the radius \(r=\frac{d}{2}=\frac{21}{2}=10.5\space yd\), and \(h = 8\space yd\).
Substitute into the formula: \(V=\pi\times(10.5)^{2}\times8=\pi\times110.25\times8=882\pi\space yd^{3}\approx882\times3.14 = 2779.5\space yd^{3}\)

Step4: Find the radius for the third cylinder (Exercise 12)

Given the radius \(r = 2\space cm\), and \(h = 13.3\space cm\).
Substitute into the formula: \(V=\pi\times(2)^{2}\times13.3=\pi\times4\times13.3 = 53.2\pi\space cm^{3}\approx53.2\times3.14=167.1\space cm^{3}\)

Answer:

Exercise 10: \(2260.8\space mm^{3}\), Exercise 11: \(2779.5\space yd^{3}\), Exercise 12: \(167.1\space cm^{3}\)