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Chapter 1: Problem 40

Solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? \(V=\frac{1}{3} B h\) for \(B\)

Short Answer

Expert verified
The formula solved for \(B\) is \(B = \frac{3V}{h}\). This formula describes the base area of a pyramid or cone, given its volume \(V\) and height \(h\).

Step by step solution

01

Identify the Variable to Solve for

We are solving for \(B\). This requires isolation of \(B\). The equation given, \(V = \frac{1}{3} B h\), shows how the variables \(V\), \(B\), and \(h\) are related.
02

Isolate B

To isolate \(B\), we have to eliminate the fractions and get rid of \(h\). Therefore, we multiply both sides of the equation by \(3\) and divide by \(h\), which gives: \(B = \frac{3V}{h}\).
03

Final Equation

The final equation, on simplification, becomes \(B = \frac{3V}{h}\), where \(B\) represents the base area of the pyramid or cone.

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Most popular questions from this chapter

In Exercises 122鈥�133, use the strategy for solving word problems, modeling the verbal conditions of the problem with a linear inequality. A company manufactures and sells blank audio cassette tapes. The weekly fixed cost is 10.000 dollar and it costs 0.40 dollar to produce each tape. The selling price is 2.00 dollar per tape. How many tapes must be produced and sold each week for the company to generate a profit?

Find all values of \(x\) satisfying the given conditions. $$ y_{1}=x-3, y_{2}=x+8, \text { and } y_{1} y_{2}=-30 $$

Find all values of \(x\) satisfying the given conditions. $$ y_{1}=\frac{2 x}{x+2}, y_{2}=\frac{3}{x+4}, \text { and } y_{1}+y_{2}=1 $$

Solve for \(t: \quad s=-16 t^{2}+v_{0} t\).

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