Question

a circus tent has the dimensions shown above. what is the surface area of the tent, not including the floor? What is the volume of the circus tent

Answer 1

Step-by-step explanation:

a) Here, we want to calculate the surface area of the tent excluding the floor

From the diagram, we have 2 triangles (height 24 ft, base 16 ft)

We also have 2 rectangles of (25 ft by 40 ft)

We have the area of the triangle as follows:

`\begin{gathered} A\text{ = }(1)/(2)* b* h \\ \\ A\text{ = }(1)/(2)*24*16\text{ = 192 ft}^2 \\ \\ Since\text{ they are two, we have:} \\ 2*\text{ 192 ft}^2\text{ = 384 ft}^2 \end{gathered}`

For the rectangles, we have:

`\begin{gathered} A\text{ = l }*\text{ b} \\ A=\text{ 25 }*\text{ 40 = 1000 ft}^2 \\ Since\text{ they are 2} \\ =\text{ 2 }*\text{ 1000 = 2,000 ft}^2 \end{gathered}`

Thus, we have the area as:

`2000\text{ + 384 = 2,384 ft}^2`

b) Here, we want to calculate the volume

Let us calculate the area of the base:

`Area\text{ = 40 }*\text{ 14 = 560 ft}^2`

So, we have the total surface area as:

`2,384\text{ + 560 = 2,944 ft}^2`

The volume is the product of the height and surface area

`2,944\text{ ft}^2*\text{ 24 = 70,656 ft}^3`