Chapter 8.5, Problem 40E

### Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Chapter
Section

### Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

# Three pipes, each of radius length 4 in., are stacked as shown. What is the exact height of the stack?

To determine

To find:

The exact height of the stack.

Explanation

Formula:

Heronâ€™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.

Letâ€™s use Heronâ€™s formula to find the area of triangle.

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

Letâ€™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=12Ã—4Ã—4Ã—4

A=163 in2

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started