Question

9 multiple choice 1 point
find the volume of a cylinder (in cubic feet) which is 5 feet high and has a diameter of 16 inches. (leave answer in terms of π.)
$\frac{20}{9}pi ft^{3}$
$\frac{10}{9}pi ft^{3}$
$72pi ft^{3}$
$36pi ft^{3}$
10 multiple choice 1 point
find the height of a trapezoid if its parallel sides are 27 cm and 33 cm long and its area is $1350 cm^{2}$.
23 cm
53 cm
45 cm
43 cm

Explanation:

Question 9

Step1: Convert units

Since \(1\) foot \( = 12\) inches, the diameter \(d = 16\) inches \(=\frac{16}{12}=\frac{4}{3}\) feet. Then the radius \(r=\frac{d}{2}=\frac{2}{3}\) feet, and the height \(h = 5\) feet.

Step2: Use the volume formula for a cylinder

The volume formula for a cylinder is \(V=\pi r^{2}h\). Substitute \(r = \frac{2}{3}\) and \(h = 5\) into the formula:

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Step1: Use the area formula for a trapezoid

The area formula for a trapezoid is \(A=\frac{(a + b)h}{2}\), where \(a\) and \(b\) are the lengths of the parallel sides, and \(h\) is the height. Given \(a = 27\) cm, \(b = 33\) cm, and \(A=1350\) \(cm^{2}\).

Step2: Solve for \(h\)

We can rewrite the formula as \(h=\frac{2A}{a + b}\). Substitute \(A = 1350\), \(a = 27\), and \(b = 33\) into the formula:

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Answer:

\(\frac{20}{9}\pi\ \text{ft}^{3}\) (the first option)

Question 10