Answer:
To calculate the mass of copper needed to make the cone, we can use the following formula:
Volume of Cone = (1/3) * π * r^2 * h
where r is the radius of the base of the cone and h is the height of the cone.
Given that Allen wants the cone’s base to have a diameter of 8 cm, we can calculate that the radius of the base is 4 cm. The height of the cone is given as 10 cm.
Substituting these values into the formula above, we get:
Volume of Cone = (1/3) * π * (4 cm)^2 * 10 cm = 167.55 cubic centimeters
The density of copper is given as 8.96 grams/cubic centimeter. Therefore, we can calculate the mass of copper needed to make the cone as follows:
Mass of Copper = Volume of Cone * Density of Copper
Mass of Copper = 167.55 cubic centimeters * 8.96 grams/cubic centimeter = 1500.98 grams
Therefore, Allen will need approximately 1500.98 grams of copper to make the cone.