Q10. - Geometry

Question

Find the following.

a.Since 1 yd = 3 ft, 1 yd² = __ ft² and 1 yd³ = __ ft³

b.Since 1 ft = __ in, 1 ft² = __ in² and 1 ft³ = __ in³

c.Since 1 m = __ cm, 1 m² = __ cm² and 1 m³ = __ cm³

Step-by-Step Solution

Answer

1. Since 1 yd = 3 ft, 1 yd² = 9 ft² and 1 yd³ = 27 ft³
2. Since 1 ft = 12 in, 1 ft² = 144 in² and 1 ft³ = 1728 in³
3. Since 1 m = 100 cm, 1 m² = 10000 cm² and 1 m³ = 10⁶ cm³

Step 1. Given information.

Given,

$1\text{ yd }=3\text{\hspace{0.17em}\hspace{0.17em}ft}$.

Step 2. Explanation.

Since,

$1\text{ yd }=3\text{\hspace{0.17em}\hspace{0.17em}ft}$

Then,

$\begin{array}{c}1{\text{ yd}}^2=1\text{ yd}\times 1\text{ yd}\\ =3\text{\hspace{0.17em}\hspace{0.17em}ft}\times 3\text{\hspace{0.17em}\hspace{0.17em}ft}\\ =9{\text{\hspace{0.17em}\hspace{0.17em}ft}}^2\end{array}$

And

$\begin{array}{c}1{\text{ yd}}^3=1\text{ yd}\times 1\text{ yd}\times 1\text{ yd}\\ =3\text{\hspace{0.17em}\hspace{0.17em}ft}\times 3\text{\hspace{0.17em}\hspace{0.17em}ft}\times 3\text{\hspace{0.17em}\hspace{0.17em}ft}\\ =27{\text{\hspace{0.17em}\hspace{0.17em}ft}}^3\end{array}$

Step 1. Given information.

Given,

$1\text{ ft }=12\text{\hspace{0.17em}\hspace{0.17em}in}$

Step 2. Explanation.

Since,

$1\text{ ft }=12\text{\hspace{0.17em}\hspace{0.17em}in}$

Then,

$\begin{array}{c}1{\text{ ft}}^2=1\text{ ft}\times 1\text{ ft}\\ =12\text{ in}\times 12\text{ in}\\ =144{\text{\hspace{0.17em}\hspace{0.17em}in}}^2\end{array}$

And

$\begin{array}{c}1{\text{ ft}}^3=1\text{ ft}\times 1\text{ ft}\times 1\text{ ft}\\ =12\text{ in}\times 12\text{ in}\times 12\text{ in}\\ =1728{\text{\hspace{0.17em}\hspace{0.17em}in}}^3\end{array}$

Step 1. Given information.

Given,

$1\text{ m }=100\text{\hspace{0.17em}\hspace{0.17em}cm}$

Step 2. Explanation.

Since,

$1\text{ m }=100\text{\hspace{0.17em}\hspace{0.17em}cm}$

Then,

$\begin{array}{c}1{\text{ m}}^2=1\text{ m}\times 1\text{ m}\\ =100\text{\hspace{0.17em}\hspace{0.17em}cm}\times 100\text{\hspace{0.17em}\hspace{0.17em}cm}\\ =10000{\text{\hspace{0.17em}\hspace{0.17em}cm}}^2\end{array}$

And

$\begin{array}{c}1{\text{ m}}^3=1\text{ m}\times 1\text{ m}\times 1\text{ m}\\ =100\text{\hspace{0.17em}\hspace{0.17em}cm}\times 100\text{\hspace{0.17em}\hspace{0.17em}cm}\times 100\text{\hspace{0.17em}\hspace{0.17em}cm}\\ =1000000{\text{\hspace{0.17em}\hspace{0.17em}cm}}^3\\ ={10}^6{\text{\hspace{0.17em}\hspace{0.17em}cm}}^3\end{array}$