Question

The lateral surface area S of a right circular cone is given by (equation given below). What radius should be used to produce a cone of height 5 inches and lateral surface area 100 square inches?
a. r = 1.52138.
b. r = 4.658
c. r = 78
d. r = 6.7432

Answer 1

Given:
Lateral Area = π * r * (√h² + r²)

Lateral Area = 100 in² ; height = 5 in

I find it hard to derive the formula of r because of the radical sign. So, I'll just plug each radius to the formula to check confirm the given lateral area.

a) r = 1.52138 ⇒ LA = 24.98
b) r = 4.658 ⇒ LA = 100 
c) r = 78 ⇒ LA = 19152.68
d) r = 6.7432 ⇒ LA = 177.84

The radius is B.) r = 4.658 inches

Answer 2

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