If the diameter is 48cm then the radius is 24cm because the diameter is two times the radius. If you know the radius and surface area, you can use the surface area formula of a cone to find the missing variable, which in this case is the slant height. The formula for finding the surface area of a cone is (pi)rl+(pi)r^2. the r^2 means r squared and the "l" is the letter used to represent the slant height and the (pi) represents the pi (3.14). Now that you have the formula all you have to do is enter the information you know in order to find the variable. Plug in the radius (24cm) and since you know the surface area plug that in as well. The equations is now 7,012=?(24)l+?(24)^2. Multiply 24 times pi and square 24 then multiply it by pi. You should get 7.012=75.36l+1,808.36. Subtract 1,808.36 from both sides to get 5,203.36=75.36l. Now all you have to do is divide both sides by 75.36 in order to get the slant height (l). The slant height is 69.047cm. Hope that helped!
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