Question

The surface area of a square pyramid can be calculated using the equation S=12lp+B
. Rearrange the surface area equation for the quantity of interest B
.(1 point)
B=

Answer 1

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 2

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 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:

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