Question

a cone has a volume of 50π cm³ and the same radius and height as a cylinder. what is the cylinders volume?
o a. 100π cm³
o b. 50π cm³
o c. 75π cm³
o d. 150π cm³

if the radius of a cylinder is 5 cm and the height is 10 cm, what is the volume?
o a. 50π cm³
o b. 25π cm³
o c. 100π cm³
o d. 250π cm³

a cone and a cylinder share the same height and radius. if the cones volume is 100 cm³, what is the cylinders volume?
o a. 300 cm³
o b. 50 cm³
o c. 33.33 cm³
o d. 200 cm³

the value of π is approximately what?
o a. 214
o b. 3.71
o c. 271
o d. 3.14

the volume of a cone with a radius of 4 cm and height of 9 cm is?
o a. 72π
o b. 48π
o c. 36π

Explanation:

First Question

Step1: Recall the volume formulas

The volume formula of a cone is \(V_{cone}=\frac{1}{3}\pi r^{2}h\), and the volume formula of a cylinder is \(V_{cylinder}=\pi r^{2}h\). If a cone and a cylinder have the same radius \(r\) and height \(h\), then \(V_{cylinder} = 3V_{cone}\).

Step2: Calculate the cylinder's volume

Given \(V_{cone}=50\pi\space cm^{3}\), then \(V_{cylinder}=3\times50\pi=150\pi\space cm^{3}\).

Second Question

Step1: Use the cylinder volume formula

The volume formula of a cylinder is \(V=\pi r^{2}h\). Given \(r = 5\space cm\) and \(h=10\space cm\), substitute into the formula: \(V=\pi\times5^{2}\times10\).

Step2: Simplify the expression

\(V=\pi\times25\times 10=250\pi\space cm^{3}\).

Third Question

Step1: Use the relationship between cone and cylinder volumes

Since \(V_{cylinder} = 3V_{cone}\) (when they have the same radius and height). Given \(V_{cone}=100\space cm^{3}\), then \(V_{cylinder}=3\times100 = 300\space cm^{3}\).

Fourth Question

Step1: Know the value of \(\pi\)

The value of \(\pi\approx3.14\).

Fifth Question

Step1: Use the cone volume formula

The volume formula of a cone is \(V=\frac{1}{3}\pi r^{2}h\). Given \(r = 4\space cm\) and \(h = 9\space cm\), substitute into the formula: \(V=\frac{1}{3}\pi\times4^{2}\times9\).

Step2: Simplify the expression

First, \(4^{2}=16\), then \(\frac{1}{3}\times16\times9=\frac{1}{3}\times144 = 48\), so \(V = 48\pi\).

Answer:

1. d. \(150\pi\space cm^{3}\)
2. d. \(250\pi\space cm^{3}\)
3. a. \(300\space cm^{3}\)
4. None of the options (the correct value of \(\pi\approx3.14\))
5. b. \(48\pi\)