Question

Основою прямої призма єпрямокутник, одна із сторін якого 15см., а діагональ 18 См. Знайти об'єм призми якщо її висота 10 См.

Answer 1

Ищем вторую сторону через формулу 
квадрат гипотенузы равен сумме квадратов катетов
здесь диагональ - гипотенуза, катеты длина и ширина
V(18х18-15х15)=V99=9,95 см - ширина
Объем равен 
9,95х15х10=1492,5 см3

Answer 2

Calculation of the Volume of a Prism

To find the volume of a prism, we need to multiply the area of the base by the height of the prism. In this case, the base of the prism is a rectangle, and the height is given as 10 cm.

To calculate the area of the base, we can use the formula for the area of a rectangle: Area = length × width.

Given that one side of the rectangle is 15 cm and the diagonal is 18 cm, we can use the Pythagorean theorem to find the other side of the rectangle.

Let's denote the width of the rectangle as w. According to the Pythagorean theorem, we have:

w^2 + 15^2 = 18^2

Simplifying the equation, we get:

w^2 + 225 = 324

Subtracting 225 from both sides, we have:

w^2 = 99

Taking the square root of both sides, we find:

w ≈ 9.95 cm

Now that we know the length and width of the base, we can calculate the area:

Area = length × width = 15 cm × 9.95 cm ≈ 149.25 cm^2.

Finally, we can calculate the volume of the prism by multiplying the area of the base by the height:

Volume = Area × height = 149.25 cm^2 × 10 cm = 1492.5 cm^3.

Therefore, the volume of the prism is approximately 1492.5 cm^3.

Please note that the calculations provided are based on the information given in the question.