Find the volume and area of the outer surface of the tank without the cap, (length 90, width 70, height 80).

Find the volume and area of the outer surface of the tank without the cap, (length 90, width 70, height 80). How much paint is needed to paint this tank from the outside and from the inside, if you need 2 g of paint to paint 1 dm2? How many liters of gasoline can I put into this tank?

1) First, we find the volume of the tank, for this all three dimensions must be multiplied, that is:

V = a * b * c = 90 * 70 * 80 = 504000 (cm ^ 3);

2) Now we find the area of ​​the outer surface, for this we find the area of ​​the base of the cylinder and the areas of the lateral sides:

S = 90 * 70 + 2 * (80 * 90 + 80 * 70) = 6300 + 2 * (7200 + 5600) = 6300 + 2 * 12800 = 6300 + 25600 = 31900 (cm ^ 2);

3) We translate: 1 dm ^ 2 = 100 cm ^ 2, then for painting 1 cm ^ 2 2/100 = 1/50 g of paint will be required;

4) Let’s calculate how much paint is required to paint the tank, for this we multiply the area by 2 (since we need to find out how much paint is required, what to paint outside and inside) and multiply by 1/50 g:

31900 * 2 * (1/50) = 1276 (g);

5) To find out how many liters of gasoline can be poured into this tank, the volume must be divided by 1000:

504000/1000 = 504 (l).

Answer: 504000 cm ^ 3, 31900 cm ^ 2, 1276 g, 504 l.