Chapter 12, Problem 7RP

To determine

To calculate: The volume of concrete needed to construct a staircase.

Answer to Problem 7RP

The volume of concrete needed is $562500c{m}^3$ .

Explanation of Solution

Given information:

A concreate staircase consists of each step of 15 cm high, 25 cm deep, and 1 cm wide. The top platform is square.

Formula used:

Volume of rectangle $=l\times w\times h$

l = length of rectangle, w = width of rectangle and h = height of rectangle

Calculation:

  

Use the divide and conquer method.

Volume of rectangle 1 $=l\times w\times h$

Volume of rectangle 1 $=100\times 25\times 15$

Volume of rectangle 1 $=37500c{m}^3$

Volume of rectangle 2 $=l\times w\times h$

Volume of rectangle 2 $=100\times 25\times \left(15+15\right)$

Volume of rectangle 2 $=100\times 25\times \left(30\right)$

Volume of rectangle 2 $=75000c{m}^3$

Volume of rectangle 3 $=l\times w\times h$

Volume of rectangle 3 $=100\times 100\times \left(15+15+15\right)$

Volume of rectangle 3 $=100\times 100\times \left(45\right)$

Volume of rectangle 3 $=450000c{m}^3$

Volume of concreate = Volume of rectangle 1 + Volume of rectangle 2 + Volume of rectangle 3

Volume of concreate $=37500+75000+450000$

Volume of concreate $=562500c{m}^3$