Question

the cylindrical tank inside a water heater has a diameter of 19.2 inches and a height of 31.1 inches. how many gallons of water does it hold? (hint: find the volume in cubic inches and then use dimensional analysis to convert to gallons. 1 gal = 231 cubic inches.) use 3.14 for pi and round your answer to the nearest tenth of a gallon. do not include a unit of measure with your response. 13 formula 0.5 points find the surface area of a box that has a length of 21.1 cm, a width of 20 cm, and a height of 26.7 cm. round your answer to the nearest hundredth, but do not include \cm²\ with your response.

Explanation:

Step1: Calculate the radius of the cylinder

The diameter $d = 19.2$ inches, so the radius $r=\frac{d}{2}=\frac{19.2}{2}=9.6$ inches.

Step2: Calculate the volume of the cylinder

The volume formula for a cylinder is $V=\pi r^{2}h$. Using $\pi = 3.14$, $r = 9.6$ inches and $h = 31.1$ inches. So $V=3.14\times9.6^{2}\times31.1=3.14\times92.16\times31.1 = 3.14\times2866.176=9009.79264$ cubic - inches.

Step3: Convert the volume from cubic - inches to gallons

Since $1$ gal $= 231$ cubic inches, the number of gallons $n=\frac{V}{231}=\frac{9009.79264}{231}\approx38.6$.

(for the second part):

Step1: Recall the surface - area formula for a rectangular prism

The surface - area formula of a rectangular prism (box) is $SA = 2(lw+lh+wh)$, where $l = 21.1$ cm, $w = 20$ cm and $h = 26.7$ cm.

Step2: Calculate $lw$, $lh$ and $wh$

$lw=21.1\times20 = 422$, $lh=21.1\times26.7 = 563.37$, $wh=20\times26.7 = 534$.

Step3: Calculate the surface area

$SA=2(422 + 563.37+534)=2\times1519.37 = 3038.74$.

Answer:

38.6