Answer:
87 packages
Step-by-step 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)
Answer:
Step-by-step explanation:
This problem bothers on the mensuration of solid shapes, a cone
the expression for the volume of a cone is
[tex]v=\frac{1}{3} \pi r^2h[/tex]
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
[tex]v=\frac{1}{3} *3.142*9^2*28\\\v= \frac{7126.056}{3}\ \\v= 2375.35cm^3\\\\[/tex]
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 = [tex]l^3= 3^3= 27cm^3\\[/tex]
now the volume of a pack is [tex]27cm^3[/tex], hence the amount of packs needed to fill the cone is calculated as,
[tex]=\frac{2375.35}{27}\\ = 87.97 packs[/tex]
