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# 28.3: D1.03: Examples 6–9

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### Example 6

Find the area of this trapezoid, where the numbers represent feet.

The formula is $A=\frac{1}{2}h\left({{b}_{1}}+{{b}_{2}}\right)$where h is the height,

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and
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are the lengths of the two bases, and A is the area. Notice that the subscripts are used because both these sides are called bases, so b is a reasonable letter to use, but there are two different ones. We use subscripts on the b’s to distinguish between the two different bases.

### Example 7

Find the volume of a sphere with radius 3 inches. The formula is $V=\frac{4}{3}\pi{{r}^{3}}$.

[hidden-answer a=”603839″]$V=\frac{4}{3}\pi{{r}^{3}}=\frac{4}{3}\pi{{\left(3\right)}^{3}}=\frac{4}{3}\pi\cdot27=113.097$.

So the volume of this sphere is 113.097 cubic inches.

### Example 8

Graph the formula $V=\frac{4}{3}\pi{{r}^{3}}$ for the values of r from 0 to 6 feet and use the graph to approximate what radius will give a volume of 400 cubic feet.

Notice that r is the input value and V is the output value.

r V
0 0
1 4.188787
2 33.51029
3 113.0972
4 268.0823
5 523.5983
6 904.7779

Using the graph, we follow the line for 400 on the vertical axis across to the graph and then down to see the corresponding r value, which is approximately $r=4.5$ feet. We can check this by plugging in and finding that $V=\frac{4}{3}\pi{{(4.5)}^{3}}=381.7$

If we wanted to get a better estimate, we would try a somewhat higher value for r.

### Example 9

Consider the problem of Example 8. Use graphical and numerical methods to find a value for the radius that will give a volume of 400 cubic feet, correct to within 10 cubic feet.

The graph tells us that a good estimate for the radius is 4.5 feet. Next we check that by plugging in and finding that   $V=\frac{4}{3}\pi{{(4.5)}^{3}}=381.7$cubic feet.   That’s a bit too low, so let’s try a slightly larger value for the radius. Let’s try 4.6 feet.   $V=\frac{4}{3}\pi{{(4.6)}^{3}}=407.72$ cubic feet.   That’s an adequate answer, according to the tolerance level stated in the problem.   Of course, if we wanted a more accurate answer, we could continue to work numerically by taking a value for the radius just a bit smaller than 4.6 feet and finding the volume for that.