Question

Около цилиндра,высота которого равна 20 см,описан прямой параллепипед. Его основанием является ромб,диагонали которого равны 12 и 16 см. Найти радиус основания цилиндра,площадь боковой поверхности цилиндра и площаль боковой поверхности параллепипеда. Я нашла лишь площадь бок. поверхности параллепипеда,она равна 800. Дальше не знаю,на что обратить внимание(

Answer 1

Аз описан около цилиндра то боковые стороны (высоты) равны а радиус основания цилиндра равен половине стороны основания параллелепипеда. и раз описан около цилиндра то в основании параллелепипеда квадрат
значит объем= Площадь основания * Высота
объем= 16*16*8=2048 (см в кубе)

Answer 2

Problem Analysis

We are given a cylinder with a height of 20 cm, and its base is a rhombus with diagonals measuring 12 cm and 16 cm. We need to find the radius of the base of the cylinder, the lateral surface area of the cylinder, and the lateral surface area of the parallelepiped.

Finding the Radius of the Base of the Cylinder

To find the radius of the base of the cylinder, we can use the formula for the area of a rhombus. The area of a rhombus can be calculated using the formula: Area = (d1 * d2) / 2, where d1 and d2 are the lengths of the diagonals.

In this case, the diagonals of the rhombus are given as 12 cm and 16 cm. Substituting these values into the formula, we can find the area of the rhombus. Since the base of the cylinder is a rhombus, the area of the rhombus will be equal to the area of the base of the cylinder.

Let's calculate the area of the rhombus (and the base of the cylinder) using the given diagonals.

Calculation

The area of the rhombus (and the base of the cylinder) can be calculated as follows:

Area = (d1 * d2) / 2

Substituting the given values:

Area = (12 cm * 16 cm) / 2

Simplifying:

Area = 192 cm²

Therefore, the area of the base of the cylinder is 192 cm².

To find the radius of the base of the cylinder, we can use the formula for the area of a circle. The formula for the area of a circle is: Area = π * r², where r is the radius of the circle.

In this case, we know the area of the base of the cylinder is 192 cm². Substituting this value into the formula, we can solve for the radius.

Calculation

The formula for the area of a circle can be rearranged to solve for the radius:

Area = π * r²

Rearranging the formula:

r² = Area / π

Substituting the given value for the area of the base of the cylinder:

r² = 192 cm² / π

Simplifying:

r² ≈ 61.11 cm² / π

Taking the square root of both sides:

r ≈ √(61.11 cm² / π)

Calculating the approximate value:

r ≈ 4.95 cm

Therefore, the radius of the base of the cylinder is approximately 4.95 cm.

Finding the Lateral Surface Area of the Cylinder

The lateral surface area of a cylinder can be calculated using the formula: Lateral Surface Area = 2πrh, where r is the radius of the base of the cylinder and h is the height of the cylinder.

In this case, we know the radius of the base of the cylinder is approximately 4.95 cm and the height of the cylinder is 20 cm. Substituting these values into the formula, we can calculate the lateral surface area of the cylinder.

Calculation

The formula for the lateral surface area of a cylinder can be calculated as follows:

Lateral Surface Area = 2πrh

Substituting the given values:

Lateral Surface Area = 2π * 4.95 cm * 20 cm

Simplifying:

**Lateral Surface