Answer:
The correct answer in each case is:
- Surface area = 60 [tex]cm^{2}[/tex]
- Surface area = 6000 [tex]mm^{2}[/tex]
- Surface area = 0.006 [tex]m^{2}[/tex]
- Volume = 1200 [tex]cm^{3}[/tex]
Step-by-step explanation:
First, to calculate the surface area or the volume you must have all the measures in the same units, for the exercise we're gonna use centimeters and after we can replace the units in the answer if we need, then:
- 300 mm = 30 cm
- 40 cm
- 50 cm
- 2 dm = 20 cm
Now, to obtain the surface area of the triangle we're gonna use the next formula:
- Surface area = (base * height) / 2
And we replace the values in centimeters:
- Surface area = (30 cm * 40 cm) / 2
- Surface area = (120 [tex]cm^{2}[/tex]) / 2
- Surface area = 60 [tex]cm^{2}[/tex]
To obtain this same value now in square milimeters, you must know:
- 1 [tex]cm^{2}[/tex] = 100 [tex]mm^{2}[/tex]
Now, you must multiply:
- 60 [tex]cm^{2}[/tex] * 100 = 6000 [tex]mm^{2}[/tex]
- 60 [tex]cm^{2}[/tex] = 6000 [tex]mm^{2}[/tex]
To obtain this value now in [tex]m^{2}[/tex], you must know:
- 1 [tex]m^{2}[/tex] = 10000 [tex]cm^{2}[/tex]
You must divide:
- 60 [tex]cm^{2}[/tex] / 10000 = 0.006
- 60 [tex]cm^{2}[/tex] = 0.006 [tex]m^{2}[/tex]
By last, to obtain the volume of the piece of cake, you can use the next formula:
- Volume of the piece of cake: surface area * depth
And we replace the surface area in [tex]cm^{2}[/tex] because the answer must be in [tex]cm^{3}[/tex]:
- Volume of the piece of cake: 60 [tex]cm^{2}[/tex] * 20 cm
- Volume of the piece of cake: 1200 [tex]cm^{3}[/tex]
