Question

A cone has a lateral area of 108 in2 and a base area of 48 in2. What is the surface area of the cone? A. 60 in2 B. 140 in2 C. 128 in2 D. 156 in2

Answer 1

Based on the given data, the following formula will be useful;
Area of the base, A = pi*r^2
Lateral Area, A(l) = pi*r*sqrt of h^2 + r^2
Surface Area, A(s) = pi*r*(r+sqrt of h^2 + r^2)
Based on the given area of the base, the radius can be calculated and is equal to 3.9088 in. Based on the given lateral area, the h or the lateral edge can be calculated and is equal to 7.8785 in. Given all the information needed, and directly substituting to the above formula for surface area, SA is equal to 156 in^2 (option D)