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:

$$w=\frac{V}{l\cdot h}$$