A can of tuna fish has a diameter 11.4 cm and height 3.7 cm. Cans are packed snugly for shipping in boxes containing 4 layers of 5 rows by 7. How much empty space does each box contain?

14447 cm³

Step-by-step explanation:

Given that:

Diameter = 11.4cm

Height = 3.7cm

boxes has 4 layers ; 5 rows by 7

Hence, dimension of shipping boxes :

Height = height of can * layer = 3.7 * 4 = 14.8 cm

Length = 5 * diameter of can = 5 * 11.4 = 57cm

Width = 7 * diameter of can = 7 * 11.4 = 79.8 cm

Volume of shipping boxes :

Height * Length * Width

14.8 * 57 * 79.8 = 67319.28 cm³

For fish can:

Radius = diameter / 2 = 11. 4 / 2 = 5.7cm

Volume (V) of can = pi*radius^2*height

V = π * 5.7^2 * 3.7 = 377.66027 cm³

Total volume of cans = number of cans * V

Total volume of cans = (4 * 5 * 7 * 377.66027)

Total volume of cans = 52872.4378 cm³

Empty space = difference in volume

= 67319.28 - 52872.4378

= 14446.8422

= 14447 cm³ (approx)

something that characterises a right triangle is the fact that we may use pythagoras' theorem to find any one of its sides given that we have the length of the other two sides. here, we have the length of the hypotenuse, √(87) yd, and one other side, √(23) yd, thus we can easily find the length of the remaining side using pythagoras' theorem as defined below:

c^2 = a^2 + b^2, where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

thus, given that c = √(87) and a = √(23), we may substitute these into the formula we defined above to get:

c^2 = a^2 + b^2

(√87)^2 = (√23)^2 + b^2 (substitute c = √87 and a = √23 into the equation)

87 = 23 + b^2 (evaluate (√87)^2 = 87 and (√23)^2 = 23 - remember that the square root of a number, squared will equal that very same number)

64 = b^2 (subtract 23 from both sides)

√64 = b (take the square root of both sides)

8 = b (evaluate √64 = 8)

therefor, the length of the unknown leg in the right triangle is 8 yd (first answer).