Question

Volume and surface area word pr 30 cm BS 30 cm Co What is the volume inside the kite? cm3 13

Answer 1

Explanation

Let's make a drawing of the situation of the exercise.

Oliver covered the 4 sides of the kite with 7200 cm^2 of ... If we define x:= Area of each side, we get

$4x=7200\operatorname{cm}^2\text{.}$

Solving this equation for x, we get

$\begin{gathered} x=\frac{7200}{4}cm^2, \\ x=1800\operatorname{cm}^2\text{.} \end{gathered}$

Now, let's recall the formula for the area (A) of a rectangle:

$A=a\cdot b\leftarrow\begin{cases}a=\text{ width} \\ b=\text{ Length}\end{cases}\text{.}$

Let's choose any side of the kite and define h to be the height of the kite. Note that h is also the width of the chosen side. Besides, its width is given; it's 30 cm. Then, we get the equation

$1800cm^2=h\cdot(30\operatorname{cm})\text{.}$

Solving this equation for h, we get

$h=\frac{1800\operatorname{cm}}{30\operatorname{cm}}=60\operatorname{cm}.$

Hence, the height of the kite is 60 cm.

Now, the volume inside the kite (V) is given by

$V=(\text{Area of the base})\cdot(height).$

Applying this formula to our case, we get

$\begin{gathered} V=(30\operatorname{cm}\cdot30\operatorname{cm})\cdot(60\operatorname{cm}), \\ V=54000\operatorname{cm}^3\text{.} \end{gathered}$Answer

The volume inside the kite is

$54000\operatorname{cm}^3.$