iamimofmonstax
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A cylindrical water tank's height is 48 feet and the diameter is 30 feet. Considering that 1 cubic yard = 202 gallons, how many gallons are in the tank when filled to capacity?

Respuesta :

MathPhys

Answer:

253,841 gallons

Step-by-step explanation:

Volume of a cylinder is:

V = π r² h

where r is the radius (half the diameter), and h is the height.

We're given r = 30 ft / 2 = 15 ft, and h = 48 ft.  Let's convert to yards:

r = 15 ft × (1 yd / 3ft) = 5 yd

h = 48 ft  × (1 yd / 3ft) = 16 yd

Plugging in:

V = π (5 yd)² (16 yd)

V = 1256.6 yd³

Converting to gallons:

V = 1256.6 yd³ × (202 gal / yd³)

V = 253840.7 gal

Rounded to the nearest gallon, the tank's capacity is 253,841 gallons.

since we know the diameter is 30 feet, then its radius is half that or 15 feet.

[tex]\bf \textit{volume of a cylinder}\\\\ V=\pi r^2 h \begin{cases} r=&radius\\ h=&height\\ \cline{1-2} r=&15~ft\\ &5~yd\\ h=&48~ft\\ &16~yd \end{cases}\implies V=\pi (5)^2(16)\implies V=400\pi ~yd^3 \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{ccll} yd^3&gallons\\ \cline{1-2} 1&202\\ 400\pi &x \end{array}\implies \cfrac{1}{400\pi }=\cfrac{202}{x}\\\\\\ x=(400\pi )(202)\implies x\approx 253840.69[/tex]