Question

Конусообразную заготовку, радиус основания которой 3 √2 дм, а высота -6 дм. переплавили в шары радиуса 2 см. Сколько получилось шаров?

Answer 1

Ответ:

из конуса получилось 216 шаров

Объяснение:

Теория:

V = (πR²h)/3 - объём конуса

V = (4πR³)/3 - объём шара

2 см = 0,5 дм

Решение:

1)  $\displaystyle \frac{\pi *(3\sqrt{2})^2*6 }{3}=\pi *18*2=36\pi$ - объём конуса
2) $\displaystyle 36\pi:\frac{4\pi *(0,5)^3}{3} =36\pi *\frac{3}{4\pi *0,125} =\frac{36*3}{0,5}=108*2= 216$

Answer 2

Calculation of the Number of Spheres

To calculate the number of spheres obtained from melting a cone-shaped blank, we need to find the volume of the cone and the volume of each sphere.

The volume of a cone can be calculated using the formula:

Volume of Cone = (1/3) * π * r^2 * h

where: - r is the radius of the base of the cone - h is the height of the cone

Given that the radius of the base of the cone is 3√2 dm and the height is 6 dm, we can substitute these values into the formula to find the volume of the cone.

Volume of Cone = (1/3) * π * (3√2)^2 * 6

Simplifying this expression, we get:

Volume of Cone = 6π * 18

Now, let's calculate the volume of each sphere. The volume of a sphere can be calculated using the formula:

Volume of Sphere = (4/3) * π * r^3

Given that the radius of each sphere is 2 cm, we can substitute this value into the formula to find the volume of each sphere.

Volume of Sphere = (4/3) * π * 2^3

Simplifying this expression, we get:

Volume of Sphere = (4/3) * π * 8

To find the number of spheres obtained, we divide the volume of the cone by the volume of each sphere:

Number of Spheres = (Volume of Cone) / (Volume of Sphere)

Now, let's substitute the values we calculated into this formula:

Number of Spheres = (6π * 18) / ((4/3) * π * 8)

Simplifying this expression, we get:

Number of Spheres = (6 * 18) / (4/3 * 8)

Number of Spheres = 108 / (32/3)

To divide a fraction by another fraction, we multiply the first fraction by the reciprocal of the second fraction:

Number of Spheres = 108 * (3/32)

Simplifying this expression, we get:

Number of Spheres = 9

Therefore, the number of spheres obtained from melting the cone-shaped blank is 9.