Question

use the data below to answer each question. use the shape tool to circle each correct choice or use the typing tool to answer the question. raul is filling his cylindrical drinking glass with soda. the formula below can be used to find the volume of the glass. v = πr²h he knows the total volume of the glass is 19 cm³, and the height of the glass is 3.5 cm, but he wants to find the radius of the glass. which of the following represents the formula solved for r? a. r = √(v/πh) b. r = √vπh c. r = vπh/2 d. r = vπh which of the following represents the formula solved for h? a. h = vπr² b. h = √(v/πr²) c. h = v/πr² d. h = √(v/πr) using your formula from #1 and the information given, find the radius of the glass. round your answer to the nearest tenth.

Explanation:

Step1: Solve the volume - formula for \(r\)

Given \(V=\pi r^{2}h\), first divide both sides by \(\pi h\): \(\frac{V}{\pi h}=r^{2}\). Then take the square - root of both sides: \(r = \sqrt{\frac{V}{\pi h}}\).

Step2: Solve the volume - formula for \(h\)

Given \(V=\pi r^{2}h\), divide both sides by \(\pi r^{2}\) to get \(h=\frac{V}{\pi r^{2}}\).

Step3: Find the radius using the values of \(V\) and \(h\)

We know \(V = 19\mathrm{cm}^{3}\) and \(h = 3.5\mathrm{cm}\). Substitute these values into the formula \(r=\sqrt{\frac{V}{\pi h}}\).
\[

$$\begin{align*} r&=\sqrt{\frac{19}{\pi\times3.5}}\\ &=\sqrt{\frac{19}{3.14\times3.5}}\\ &=\sqrt{\frac{19}{10.99}}\\ &=\sqrt{1.73}\\ &\approx1.3\mathrm{cm} \end{align*}$$

\]

Answer:

1. A. \(r=\sqrt{\frac{V}{\pi h}}\)
2. C. \(h=\frac{V}{\pi r^{2}}\)
3. \(1.3\mathrm{cm}\)