Chapter 12, Problem 15RP

To determine

To calculate:Thevolume of wedge with rectangular dimensions of25 and 30.

Answer to Problem 15RP

Thevolume of wedgeis $5040$ .

Explanation of Solution

Given information:

A wedge with rectangular dimensions of 25 and 30. An isosceles triangle with dimensions 25, 25 and 14.

Formula used:

The below theorem is used:

Pythagoras theorem states that “In a right angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides”.

  

In right angle triangle,

  $a^2+b^2\text{= }{c}^2$

Area of triangle: $A=\frac{1}{2}\times b\times a$

Where “b”is base of triangle

“a” is height of triangle

Volume of prism $=B\times h$

Where “B” is Base area of prism and“h” is height of prism

Calculation:

  

Draw the altitude to the base of the isosceles triangle by bisecting it.

The height h of altitude can be calculated by applying Pythagoras Theorem.

In right angled triangle, we get

  ${\left(BE\right)}^2={\left(BD\right)}^2+{\left(DE\right)}^2$

  $\begin{array}{l}{\left(25\right)}^2={\left(a\right)}^2+{\left(7\right)}^2\\ {\left(25\right)}^2={\left(a\right)}^2+{\left(7\right)}^2\\ {\left(a\right)}^2=625-49\\ {\left(a\right)}^2=576\\ a=\sqrt{576}=24\end{array}$

  $B=\frac{1}{2}\times b\times a=\frac{1}{2}\times 14\times 24=168$

Volume of prism $=B\times h$

Volume of prism $=168\times 30$

Volume of prism $=5040$