Question

exercises:
using the formula ( v=\text{length}cdot\text{width}cdot\text{height}div3 ) or ( v=\frac{1}{3}cdot\text{length}cdot\text{width}cdot\text{height} ), substitute the values given in each problem and solve.
1.)

__________cu. yd.
2.)

__________cu. ft.
3.)

__________cu. in.
complete the table for each pyramid described. you may use a calculator.
4.)
5.)
6.)
7.)
8.)

Explanation:

1.

Step1: Substitute values into formula

Given \(l = 2\) yd, \(w = 2\) yd, \(h=4\) yd. Use \(V=\frac{1}{3}lwh\).
\(V=\frac{1}{3}\times2\times2\times4\)

Step2: Calculate

\(V=\frac{16}{3}\approx5.33\) cu. yd

2.

Step1: Substitute values into formula

Given \(l = 4\) ft, \(w = 3\) ft, \(h = 2.3\) ft. Use \(V=\frac{1}{3}lwh\).
\(V=\frac{1}{3}\times4\times3\times2.3\)

Step2: Calculate

\(V = 9.2\) cu. ft

3.

Step1: Substitute values into formula

Given \(l = 8\) in, \(w = 2.5\) in, \(h = 3.5\) in. Use \(V=\frac{1}{3}lwh\).
\(V=\frac{1}{3}\times8\times2.5\times3.5\)

Step2: Calculate

\(V=\frac{70}{3}\approx23.33\) cu. in

4.

Step1: Substitute values into formula

Given \(l = 17\) in, \(w = 6\) in, \(h = 9\) in. Use \(V=\frac{1}{3}lwh\).
\(V=\frac{1}{3}\times17\times6\times9\)

Step2: Calculate

\(V = 306\) cu. in

5.

Step1: Substitute values into formula

Given \(l = 14.2\) ft, \(w = 6\) ft, \(h = 7\) ft. Use \(V=\frac{1}{3}lwh\).
\(V=\frac{1}{3}\times14.2\times6\times7\)

Step2: Calculate

\(V=198.8\) cu. ft

6.

Step1: Convert mixed - number to improper fraction

\(19\frac{1}{2}=\frac{39}{2}\). Given \(l=\frac{39}{2}\) yd, \(w=\frac{39}{2}\) yd, \(h = 12\) yd. Use \(V=\frac{1}{3}lwh\).
\(V=\frac{1}{3}\times\frac{39}{2}\times\frac{39}{2}\times12\)

Step2: Calculate

\(V = 1521\) cu. yd

7.

Step1: Convert mixed - number to improper fraction

\(6\frac{1}{2}=\frac{13}{2}\), \(8\frac{1}{2}=\frac{17}{2}\). Given \(l = 12\) ft, \(w=\frac{13}{2}\) ft, \(h=\frac{17}{2}\) ft. Use \(V=\frac{1}{3}lwh\).
\(V=\frac{1}{3}\times12\times\frac{13}{2}\times\frac{17}{2}\)

Step2: Calculate

\(V = 221\) cu. ft

8.

Step1: Convert mixed - number to improper fraction

\(9\frac{1}{4}=\frac{37}{4}\), \(2\frac{1}{2}=\frac{5}{2}\), \(4\frac{1}{4}=\frac{17}{4}\). Given \(l=\frac{37}{4}\) in, \(w=\frac{5}{2}\) in, \(h=\frac{17}{4}\) in. Use \(V=\frac{1}{3}lwh\).
\(V=\frac{1}{3}\times\frac{37}{4}\times\frac{5}{2}\times\frac{17}{4}\)

Step2: Calculate

\(V=\frac{3145}{96}\approx32.76\) cu. in

Answer:

1. \(5.33\) cu. yd
2. \(9.2\) cu. ft
3. \(23.33\) cu. in
4. \(306\) cu. in
5. \(198.8\) cu. ft
6. \(1521\) cu. yd
7. \(221\) cu. ft
8. \(32.76\) cu. in