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2 years ago

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Fruit juice comes in two types of containers. The first is a rectangular prism that is 9 inches tall and has a rectangular base

that measures 2 inches by 3 inches. The second container is a cylinder that is 8 inches tall and has a radius of 1.5 inches. Which of the following statements is valid? A. The volumes are the same. B. The prism has the greater volume. C. The cylinder has the greater volume. D. The volumes cannot be determined.

1 answer:

My name is Ann [436]2 years ago

3 0

The volume of a rectangular prism:

$V_p=Bh\\\\B=wl\\\\w=2\ in;\ l=3\ in;\ h=9\ in$

substitute

$V_p=2\cdot3\cdot9=54\ in^3$

The volume of a cylinder:

$V_c=\pi r^2h\\\\r=1.5\ in;\ h=8\ in$

substitute:

$V_c=\pi\cdot(1.5)^2\cdot8=\pi\cdot2.25\cdot8=18\pi\ in^3\approx18\cdot3.14=56.52\ in^3$

Answer: C. The cylinder has the greater volume.

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Step-by-step explanation:

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Let the height of the cliff be $h$ meters and $h= h_1+h_s$ .

Using trigonometric ratios:

tan (Ф) = opposite/adjacent

In ΔSPQ. In ΔSPR.

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Dividing equation (i) and (ii)

⇒ $\frac{tan(60)}{tan(30)} = \frac{h_1}{x} \times \frac{x+50}{h_1}$

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⇒ $2x=50$

⇒ $x=\frac{50}{2}$

⇒ $x=25$ meters

To find $h_1$ plugging $x=25$ in equation (i)

⇒ $h_1=x\times tan(60)$

⇒ $h_1=25\times 1.73$

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⇒ $h=45.05$ meters

The cliff is 45 m tall to the nearest meter.

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