Answer:
r = 4.658
Step-by-step explanation:
Height of cone = 5 inches
Curved surface area of cone =\(\pi r \times \sqrt{r^2+h^2}\)
We are given that lateral surface area is 100 square inches.
So, \(100 = 3.14 \times r \times \sqrt{r^2+5^2}\)
\(100 = 3.14 \times r \times \sqrt{r^2+25}\)
\(\frac{100}{3.14}= r \times \sqrt{r^2+25}\)
\(31.847= r \times \sqrt{r^2+25}\)
Squaring both sides
\(1014.231409= r^2 \times (r^2 +25)\)
\(1014.231409= r^4 +25r^2)\)
\(r^4 +25r^2-1014.231409=0\)
Solving this using Scientific calculator
r = 4.658
Hence the radius should be used to produce a cone of height 5 inches and lateral surface area 100 square inches is 4.658 inches
