Question

1. Find the surface area of each shape. Label each diagram and show your work. Use 3.14 for π and round

your answers to the nearest tenth if needed.

Answer 1

Explanation:

1a. Since we know this is a cuboid we can simply multiply all the numbers together

6 x 2 x 5 = 60
`m^(3)`

1b. This is a triangular prism dont let the hypotenouse (13 in) trick you since we need the perpendicular height to calculate the area of the triangle. Let's first find the area of the triangle

12 x 5 = 60

60 /2 = 30
`in^(2)`

Now since this is a prism we need to multiply the area of the front of the shape with how long it is

30 x 4 = 120
`in^(3)`

1c. This is the easiest as since we know that its a cube and the side length is 12 we can simply do

`12^(3)` = 1728
`in^(3)` we need to round this to the nearest tenth so we get

1730
`in^(3)`

1d. Lastly the volume of a cone is π
`r^(2)`
`(h)/(3)` as you notice we dont have a perpendicular height so lets find it out using pythagorus

6^2 + b^2 = 7^2

b^2 = 49 -36

b =
`√(13)`

now we have the height we can calculate its volume

(3.14) x (6)^2 x
`√(13)` /3=

140
`in^(3)` rounded to the nearest 10th