well, let's first notice, all our dimensions or measures must be using the same unit, so could convert the height to liters or the liters to centimeters, well hmm let's convert the volume of 1000 litres to cubic centimeters, keeping in mind that there are 1000 cm³ in 1 litre.

well, 1000 * 1000 = 1,000,000 cm³, so that's 1000 litres.

$\textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ V=1000000~cm^3\\ h=224~cm \end{cases}\implies \stackrel{cm^3}{1000000}=\pi r^2(\stackrel{cm}{224}) \\\\\\ \cfrac{1000000}{224\pi }=r^2\implies \sqrt{\cfrac{1000000}{224\pi }}=r\implies \cfrac{1000}{\sqrt{224\pi }}=r\implies \stackrel{cm}{37.7}\approx r$

now, we could have included the "cm³ and cm" units for the volume as well as the height in the calculations, and their simplication will have been just the "cm" anyway.

6 0

2 years ago

Geometry help please! Match the reasons with the statements.

SSSSS [86.1K]

Given:

∠PRS and ∠VUW are supplementary.

To prove:

Line TV || Line QS

Solution:

Step 1: Given

∠PRS and ∠VUW are supplementary.

Step 2: By the definition of supplementary angles

$m\angle {PRS}+m\angle {VUW}=180^{\circ}$

Step 3: Angles forming a linear pair sum to 180°

$m\angle {PRS}+m\angle {SRU}=180^{\circ}$

Step 4: By transitive property of equality

step 2 = step 3

$m\angle {PRS}+m\angle {VUW}=m\angle {PRS}+m\angle {SRU}$

Step 5: By algebra cancel the common terms in both side.

${m} \angle {VUW}={m} \angle{SRU}$

Step 6: By converse of corresponding angles postulate

Line TV || Line QS

Hence proved.

6 0

3 years ago