Question

Найдите объем и площадь поверхности прямоугольного параллелепипеда, длина, ширина и высота которого соответственно равны 2 1/3 м, 1 4/5 м, 5 3/4м решите пожалуйста

Answer 1

Объем по формуле
V = a*b*c = 2 1/3 * 1 4/5 * 5 3/4 = 24 3/20 - ОТВЕТ
Площадь поверхности (полная) по формуле
S = 2*(a*b + a*c + b*c) = 2*(4 1/5 + 13 5/12 + 10 7/20) = 2*27 29/30
= 53 14/15  - ОТВЕТ

Answer 2

Calculation of Volume and Surface Area of a Rectangular Parallelepiped

To find the volume and surface area of a rectangular parallelepiped, we need to know its length, width, and height. In this case, the given dimensions are:

- Length: 2 1/3 m - Width: 1 4/5 m - Height: 5 3/4 m

Let's calculate the volume and surface area step by step.

Calculation of Volume

The volume of a rectangular parallelepiped is given by the formula:

Volume = Length x Width x Height

Substituting the given values:

Volume = (2 1/3 m) x (1 4/5 m) x (5 3/4 m)

To simplify the calculation, we can convert the mixed fractions to improper fractions:

Volume = (7/3 m) x (9/5 m) x (23/4 m)

Now, multiply the fractions:

Volume = (7/3) x (9/5) x (23/4) m^3

To multiply fractions, multiply the numerators together and the denominators together:

Volume = (7 x 9 x 23) / (3 x 5 x 4) m^3

Calculating the numerator and denominator separately:

Numerator = 7 x 9 x 23 = 1449 Denominator = 3 x 5 x 4 = 60

Volume = 1449 / 60 m^3

Simplifying the fraction:

Volume = 24.15 m^3

Therefore, the volume of the rectangular parallelepiped is 24.15 cubic meters.

Calculation of Surface Area

The surface area of a rectangular parallelepiped is given by the formula:

Surface Area = 2(ab + bc + ac)

where a, b, and c are the lengths of the three pairs of opposite sides.

Substituting the given values:

a = 2 1/3 m b = 1 4/5 m c = 5 3/4 m

Surface Area = 2[(2 1/3 m x 1 4/5 m) + (1 4/5 m x 5 3/4 m) + (2 1/3 m x 5 3/4 m)]

Again, let's convert the mixed fractions to improper fractions:

Surface Area = 2[(7/3 m x 9/5 m) + (9/5 m x 23/4 m) + (7/3 m x 23/4 m)]

Now, multiply the fractions:

Surface Area = 2[(7/3) x (9/5) + (9/5) x (23/4) + (7/3) x (23/4)] m^2

To multiply fractions, multiply the numerators together and the denominators together:

Surface Area = 2[(7 x 9 x 4 + 9 x 23 x 3 + 7 x 23 x 5) / (3 x 5 x 4)] m^2

Calculating the numerator and denominator separately:

Numerator = 7 x 9 x 4 + 9 x 23 x 3 + 7 x 23 x 5 = 828 + 621 + 805 = 2254 Denominator = 3 x 5 x 4 = 60

Surface Area = 2(2254 / 60) m^2

Simplifying the fraction:

Surface Area = 75.133 m^2

Therefore, the surface area of the rectangular parallelepiped is 75.133 square meters.

To summarize: - The volume of the rectangular parallelepiped is 24.15 cubic meters. - The surface area of the rectangular parallelepiped is 75.133 square meters.

Please let me know if you need any further assistance!