Question

Сосуд имеет вид усеченного конуса высота которого 27 см и длины окружностей оснований равны 66 и 96. Найдите площадь боковой поверхности

Answer 1

Ответ:

14265

Объяснение:

Answer 2

Calculation of the lateral surface area of the truncated cone

To find the lateral surface area of the truncated cone, we need to know the slant height of the cone. The slant height can be calculated using the Pythagorean theorem, which states that the square of the slant height is equal to the sum of the squares of the radius and the height of the cone.

Let's denote the radius of the smaller base of the cone as r1, the radius of the larger base as r2, and the height of the cone as h.

Using the given information, we have: - Height of the cone, h = 27 cm - Circumference of the smaller base, C1 = 66 cm - Circumference of the larger base, C2 = 96 cm

To find the slant height, we can use the formula: l = sqrt((r2 - r1)^2 + h^2)

Let's calculate the slant height first:

l = sqrt((C2 / (2 * pi) - C1 / (2 * pi))^2 + h^2)

l = sqrt(((96 / (2 * pi)) - (66 / (2 * pi)))^2 + 27^2)

l ≈ 23.57 cm

Now that we have the slant height, we can calculate the lateral surface area of the truncated cone using the formula: A = pi * (r1 + r2) * l

Let's substitute the values and calculate the lateral surface area:

A = pi * (r1 + r2) * l

A = pi * ((C1 / (2 * pi)) + (C2 / (2 * pi))) * l

A = (C1 + C2) * l

A ≈ (66 + 96) * 23.57

A ≈ 3467.88 cm^2

Therefore, the lateral surface area of the truncated cone is approximately 3467.88 cm^2.

Please note that the calculations are approximate due to rounding off the values during the calculation process.