Question

Площадь полной поверхности прямоугольного параллелепипеда, в основании которого прямоугольник со сторонами 9 и 6 см, равна 408 см2. Найдите диагональ параллелепипеда

Answer 1

Площадь поверхности:2ab+ 2c(a+b) = 2*9*6+2c(6+9)=108+30c=408
30c = 300, c = 10 см 
диагональ = корень (a^2 +b^2+c^2)=корень 217

Answer 2

Calculation of the Surface Area of the Rectangular Parallelepiped

To find the diagonal of the rectangular parallelepiped, we first need to calculate the surface area of the parallelepiped.

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 sides of the parallelepiped.

In this case, the parallelepiped has a rectangular base with sides measuring 9 cm and 6 cm. The surface area is given as 408 cm².

Let's calculate the surface area:

Surface Area = 2(9 * 6 + 6 * c + 9 * c) = 408 cm².

Simplifying the equation:

Surface Area = 2(54 + 15c) = 408 cm².

108 + 30c = 408.

30c = 408 - 108.

30c = 300.

c = 300 / 30.

c = 10.

Therefore, the length of the third side of the parallelepiped is 10 cm.

Calculation of the Diagonal of the Parallelepiped

To find the diagonal of the parallelepiped, we can use the Pythagorean theorem. The diagonal is the hypotenuse of a right triangle formed by the three sides of the parallelepiped.

Let's label the sides of the parallelepiped as a, b, and c, where a and b are the lengths of the base rectangle (9 cm and 6 cm) and c is the length of the third side (10 cm).

The diagonal (d) can be calculated using the formula:

d = sqrt(a² + b² + c²).

Substituting the values:

d = sqrt(9² + 6² + 10²).

d = sqrt(81 + 36 + 100).

d = sqrt(217).

Using a calculator, we find that the square root of 217 is approximately 14.73.

Therefore, the diagonal of the rectangular parallelepiped is approximately 14.73 cm.