Question

Please help me with this question!

A​ cone-shaped vase has height 28 cm and radius 9 cm. An artist wants to fill the vase with colored sand. The sand comes in small​ packages, each of which is a cube with side length 3 cm. At most, how many packages of sand can the artist use without making the vase​ overflow?

Answer 1

87.97 packs

Explanation:

This problem bothers on the mensuration of solid shapes, a cone

the expression for the volume of a cone is

`v=(1)/(3) \pi r^2h`

Given data

height h= 28cM

radius r= 9cm

substituting the data the data into the expression for the volume we can solve for the volume

`v=(1)/(3) *3.142*9^2*28\\\v= (7126.056)/(3)\ \\v= 2375.35cm^3\\\\`

we know that a pack contains a cube, we then need to calculate the volume of a cube in a pack, given that the length of a cube is 3cm

the volume is =
`l^3= 3^3= 27cm^3\\`

now the volume of a pack is
`27cm^3`, hence the amount of packs needed to fill the cone is calculated as,

`=(2375.35)/(27)\\ = 87.97 packs`

Answer 2

87 packages

Explanation:

First we need to find the volume of the cone-shaped vase.

The volume of a cone is given by:

V_cone = (1/3) * pi * radius^2 * height

With a radius of 9 cm and a height of 28 cm, we have:

V_cone = (1/3) * pi * 9^2 * 28 = 2375.044 cm3

Each package of sand is a cube with side length of 3 cm, so its volume is:

V_cube = 3^3 = 27 cm3

Now, to know how many packages the artist can use without making the vase overflow, we just need to divide the volume of the cone by the volume of the cube:

V_cone / V_cube = 2375.044 / 27 = 87.9646 packages

So we can use 87 packages (if we use 88 cubes, the vase would overflow)