Recall that the surface area of a cone is the lateral area plus the area of the base. To calculate the surface area of a cone, we can use the following formula.
S.A.=L.A.+Ï€ r^2
In this formula, r is the radius of the base. Note that we know the lateral area and the diameter of the given cone. To find the radius, we can divide the diameter by 2.
The radius is 7.5 millimeters. Now we can substitute the lateral area and the radius into the formula and calculate the total surface area of the cone. Let's do it!
We got that the surface area of the cone is about 510.2 square millimeters.
Now we want to find the slant height of the cone. To do so, let's start by recalling that the lateral area of a cone can be calculated by using the following formula.
L.A.=Ï€ r lIn this formula, r is the radius of the base and l is the slant height of the cone. We know that the lateral area of the given cone is about 333.5 square millimeters. Moreover, in Part A, we found that the radius is 7.5 millimeters. Let's substitute these values into the formula.
L.A.=π r l [0.3em] ⇕ [0.3em] 333.5=π ( 7.5)( l)
Notice that we got an equation that will help us to find the slant height of the cone. Let's solve the equation for l.
