The surface area of a square pyramid can be calculated using the equation S=12lp+B

Question

. Rearrange the surface area equation for the quantity of interest B
.(1 point)
B=

Answer 1

To rearrange the equation for the surface area of a square pyramid, \( S = \frac{1}{2} lp + B \), for the quantity \( B \), you can follow these steps:

1. Start with the original equation: \[ S = \frac{1}{2} lp + B \]

2. Subtract \( \frac{1}{2} lp \) from both sides to isolate \( B \): \[ B = S - \frac{1}{2} lp \]

So, the rearranged equation for \( B \) is: \[ B = S - \frac{1}{2} lp \]

Answer 2

Claudia’s family is buying a new cabinet for their home. The height of the cabinet is 5 ft., its length is 4 ft., and its volume is 60 ft.3
. They need to know the width of the cabinet to make sure that it will fit in the space where they want to put it. Using the volume formula, V=lwh
, rearrange the formula to highlight the quantity of interest. Note that volume is represented with a capital V
in the formula.(1 point)
$$

Answer 3

To find the width of the cabinet using the volume formula, we start with the formula for the volume of a rectangular prism:

\[ V = l \cdot w \cdot h \]

where:

• \( V \) is the volume,
• \( l \) is the length,
• \( w \) is the width,
• \( h \) is the height.

We need to rearrange this formula to isolate \( w \):

1. Start with the original volume formula: \[ V = l \cdot w \cdot h \]

2. Divide both sides by \( l \cdot h \) to isolate \( w \): \[ w = \frac{V}{l \cdot h} \]

Now, substituting the given values \( V = 60 , \text{ft}^3 \), \( l = 4 , \text{ft} \), and \( h = 5 , \text{ft} \):

\[ w = \frac{60}{4 \cdot 5} \]

Calculating the denominator:

\[ w = \frac{60}{20} \]

Now, simplifying further gives:

\[ w = 3 , \text{ft} \]

Thus, the width \( w \) of the cabinet is 3 ft.

In conclusion, the rearranged formula is:

\[ w = \frac{V}{l \cdot h} \]