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Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

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BuyFindarrow_forward

Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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Three pipes, each of radius length 4 in., are stacked as shown. What is the height of the stack?

Chapter 8.5, Problem 40E, Three pipes, each of radius length 4 in., are stacked as shown. What is the height of the stack?

To determine

To find:

The exact height of the stack.

Explanation

Formula:

Heron’s formula for area of triangle:

If a, b and c are lengths of sides of triangle, then area of triangle is given by the formula:

A=s(s-a)(s-b)(s-c)

Where s is the semi perimeter which is given by s=12(a+b+c)

Area of triangle is also given by the formula 12bh where b is the length of base and h is the height of the triangle.

Calculation:

Three pipes are stacked in such a way that the centre of each of them can be joined to form a triangle. The radius of each pipe is given as 4 in.

The length of each side of the triangle will be the sum of radius of adjacent pipes.

Thus, the length of each side of triangle is 4+4=8 in.

It can be observed that length of side of the triangle is 8 in. Hence, the triangle is an equilateral triangle. Hence, a=b=c=8 in.

To find the exact height of the stack, we need to find the height of the triangle.

Let’s use Heron’s formula to find the area of triangle.

Semi perimeter of the triangle is s=8+8+82=242=12

Let’s substitute the value of s in the formula to find the area of triangle.

A=s(s-a)(s-b)(s-c)

A=1212-812-812-8

A=12×4×4×4

A=163 in2

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