a Use the formula for the volume of a cone.The volume of a cone is one third the product of its base area and height.
B
b Use the formula for the lateral surface area of a cone. The surface area of a right cone is the sum of the base area and the lateral area. The area of the base is given by π r^2 and the lateral area has the area π rl.
A
a Approximately 27.2 in^3
B
b About 42.7 in^2
Practice makes perfect
a Using the given information, we can draw a model of the cone-shaped hats created for the party.
Now we can use the formula for the volume of a cone to calculate the volume of the hats.
V=1/3Ï€ r^2 h
In this formula, r is the radius and h is the height of the cone. We know that the cone is 6.5 inches tall. We are also given a diameter of the cone's base. Since we need to know the radius, let's divide the diameter of 4 inches by 2.
r=4/2=2inches
Now, we can substitute the values of the radius and height into the formula, and calculate the volume.
The volume of candy that will fill the cone is approximately 27.2 in^3.
b Lawana makes the cone-shaped hats by hand, so to find the area of the material she needs, we should calculate the surface area of a cone. We can use a modified version of the formula for surface area. We do not need to include the area of the base because this is where a head will go!
SA_(cone) (including the Base)=& π rl+ π r^2
SA_(cone)(excluding the Base)=& π rl
In this formula, r is the radius and l is the slant height of the cone. We know both of them, so let's substitute these values into the formula.
