Question

радиусы оснований усеченного конуса 11 и 16 см образуюшая 13 см найти расстояние от центра меньшего основания до окружности большего основания

Answer 1

Так как нижнее основание 16, а верхнее 11, то разница между ними равна 5. Рассмотрим прямоугольный треугольник, где один из катетов 5 (т.е. разница),  а гипотенуза равна образующей, то есть 13. По сути, нам надо найти высоту конуса. По теореме Пифагора:

13^2 - 5^2 = 169 - 25 = 144, корень из 144 = 12.  

Answer 2

Given Information

We are given the following information about a truncated cone: - The radii of the bases are 11 cm and 16 cm. - The slant height (or oblique height) is 13 cm.

We need to find the distance from the center of the smaller base to the circumference of the larger base.

Solution

To find the distance from the center of the smaller base to the circumference of the larger base, we need to find the height of the truncated cone.

Let's denote the radius of the smaller base as r1 (11 cm), the radius of the larger base as r2 (16 cm), and the slant height as l (13 cm).

Using the Pythagorean theorem, we can find the height (h) of the truncated cone:

h = sqrt(l^2 - (r2 - r1)^2)

Substituting the given values, we have:

h = sqrt(13^2 - (16 - 11)^2) = sqrt(169 - 25) = sqrt(144) = 12 cm

Now, we can find the distance from the center of the smaller base to the circumference of the larger base. This distance is equal to the height of the smaller cone formed by the center of the smaller base and the larger base.

Since the smaller cone is similar to the original truncated cone, we can use the proportion:

h1 / r1 = h / r2

Substituting the values, we have:

h1 / 11 = 12 / 16

Simplifying the equation, we find:

h1 = (12 * 11) / 16 = 6.75 cm

Therefore, the distance from the center of the smaller base to the circumference of the larger base is approximately 6.75 cm.

Answer

The distance from the center of the smaller base to the circumference of the larger base is approximately 6.75 cm.