The surface area of a square pyramid can be calculated using the equation S=1/2lp+B . Rearrange the surface area equation for the quantity of interest B .(1 point)

Question

B=()

Answer 1

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

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

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

3. Therefore, the rearranged equation is: \[ B = S - \frac{1}{2}lp \]

So, the final answer 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)

w= ()/()

Answer 3

To rearrange the volume formula \( V = lwh \) to solve for the width \( w \), follow these steps:

1. Start with the original volume formula: \[ V = lwh \]

2. To isolate \( w \), divide both sides by \( lh \): \[ w = \frac{V}{lh} \]

Given Claudia’s family's cabinet dimensions:

• Height \( h = 5 \) ft
• Length \( l = 4 \) ft
• Volume \( V = 60 \) ft³

Substituting these values into our rearranged equation for \( w \):

\[ w = \frac{60 , \text{ft}^3}{4 , \text{ft} \times 5 , \text{ft}} \]

Hence, the formula for \( w \) is:

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

So, the final answer is:

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

Thus, you can write it as:

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