Question

oliver is building a box kite. the frame of the kite has the dimensions shown. he covered the sides of the kite (but not the top and bottom) with 7200 cm² of lightweight fabric.
30 cm
30 cm
what is the volume inside the kite?

Explanation:

Step1: Define lateral surface area formula

The box kite is a rectangular prism. The lateral surface area (excluding top and bottom) is given by $A = 2(lh + wh)$, where $l=30\ \text{cm}$, $w=30\ \text{cm}$, and $h$ is the unknown height. Substituting $l$ and $w$:
$A = 2(30h + 30h) = 2(60h) = 120h$

Step2: Solve for height $h$

Set the lateral surface area equal to $7200\ \text{cm}^2$:
$120h = 7200$
$h = \frac{7200}{120} = 60\ \text{cm}$

Step3: Calculate volume of the prism

Volume formula for a rectangular prism is $V = lwh$. Substitute $l=30$, $w=30$, $h=60$:
$V = 30 \times 30 \times 60$

Answer:

$54000\ \text{cm}^3$