A glass vase is in the shape of a cylinder with a cone shaped opening. The height of the cylinder is 33 cm and the diameter is 20 cm. How much glass is needed to make the vase?

Question

Ella Armstrong · Accepted Answer

The amount of glass required is #2200picm^3# or #6908cm^3#.

Presuming the height of the cone also to be #33cm# (the presumption being that the tip of the cone-shaped opening is at the other end of the cylinder), and that the diameter is the same for both, the method we use is to subtract the volume of the cone from the volume of the cylinder - that will give us the volume of glass required. Hence: #Vg=Vcy-Vco# The formula for volume of a cylinder is: #Vcy=pir^2h#, where #r=#radius, and #h=#height. The formula for volume of a cone is: #Vco=pir^2h/3# Hence: #Vg=Vcy-Vco# #Vg=pir^2h-pir^2h/3# #Vg=pir^2h(1-1/3)# #Vg=pir^2h(2/3)# #Vg=pixx10^2xx33xx2/3# Substitute #10# for #r# (radius is half the diameter), and #33# for #h#. #Vg=pixx100xx11cancel33xx2/(1cancel3)# #Vg=pixx100xx11xx2# #Vg=pixx2200# #Vg=2200pi# Considering #pi=3.14#: #Vg=6908#

Jayden Jackson · Answer

undefined To find the amount of glass needed to make the vase, we need to calculate the surface area of both the cylinder and the cone-shaped opening.

First, let's calculate the surface area of the cylinder. The formula for the surface area of a cylinder is:

Surface Area of Cylinder = 2πr^2 + 2πrh

Given that the diameter of the cylinder is 20 cm (which means the radius, r, is half of that, so r = 10 cm), and the height, h, is 33 cm, we can plug these values into the formula to find the surface area of the cylinder.

Next, let's calculate the surface area of the cone-shaped opening. The formula for the surface area of a cone is:

Surface Area of Cone = πr*l

Where r is the radius of the base of the cone, and l is the slant height.

To find the slant height, we can use the Pythagorean theorem. The slant height (l) is the hypotenuse of a right triangle formed by the height of the cylinder (33 cm) and the radius of the cylinder (10 cm).

Slant Height (l) = √(h^2 + r^2)

Once we have the slant height, we can plug it into the formula for the surface area of the cone to find the surface area of the cone-shaped opening.

Finally, to find the total amount of glass needed to make the vase, we add the surface area of the cylinder to the surface area of the cone-shaped opening.