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Chapter 7: Problem 13

In Exercises \(10-13,\) find the approximate circumference and area of each circle with the given radius or diameter using the calculator to approximate the answer to the nearest hundredth. \(d=18.36 \mathrm{yd}\)

Short Answer

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Step by step solution

01

- Find the Radius

The given diameter is 18.36 yards. The formula to find the radius from the diameter is ............
02

- Find the Circumference

Use the formula for calculating the circumference of a circle, which is ...........
03

- Find the Area

Use the formula to calculate the area of a circle, which is ...

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Circumference Calculation
The circumference of a circle is essentially the perimeter or the distance around the circle. To find the circumference, use the formula: \(C = \pi \times d\) for the diameter or \(C = 2 \pi r\) for the radius. Here, \pi (pi)\ is approximately 3.14.

Let's break this down:
  • If you know the diameter (\

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Most popular questions from this chapter

How much more cross-sectional area is there for water to pass through in a \(\frac{3}{4}\) -inch-diameter water hose than there is in a \(\frac{1}{2}\) -inch-diameter water hose? Round to the nearest hundredth.

Find the area of a sector of a circle if the radius is 12.6 inches and the arc of the sector is \(25^{\circ}\). Give the answer correct to the nearest tenth of a square inch.

A 12 -inch-diameter pizza costs \(\$ 10.00 .\) A 16 -inch-diameter pizza costs \(\$ 12.00 .\) Which pizza costs less per square inch? Use the \([\pi]\) key on the calculator if necessary.

The area of a sector of a circle is \(24 \pi\) yd \(^{2}\). If the arc of the sector is \(60^{\circ}\), find the diameter of the circle.

Brahmagupta was an East Indian mathematician who lived during the seventh century. He discovered a formula for the area of a quadrilateral inscribed within a circle. As we learned in Chapter \(6,\) this means the vertices of the quadrilateral lie on the circle. \(A=\sqrt{(s-a)(s-b)(s-c)(s-d)},\) where \(a, b, c,\) and \(d\) are the lengths of the sides of the quadrilateral and \(s=\frac{a+b+c+d}{2}\) This formula looks similar to Heron's formula for the area of a triangle. Discuss the similarities and differences. Show a numerical example of how the formula works. Research more about the life of Brahmagupta.
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