# FIND SLANT HEIGHT OF CONE GIVEN SURFACE AREA AND RADIUS

To find lateral surface area and total surface area of cone, we use the formulas given below.

Lateral surface area =  πrl

Total surface area =  πrl +  πr2

πr(l + r)

Here r = radius, l = slant height

Find slant height of the following cones given below.

Problem 1 :

Solution :

Total surface area πr(l + r)

πr(l + r) = 33π

3π(l + 3) = 33π

3(l + 3) = 11

Subtracting 3 on both sides.

l = 11 - 3

l = 8

So, the required slant height is 8 inches.

Problem 2 :

Solution :

Total surface area = πr(l + r)

πr(l + r) = 126π

diameter = 12 cm

6π(l + 6) = 126π

6(l + 6) = 126

Dividing by 6 on both sides.

l + 6 = 21

Subtracting 6 on both sides.

l = 21 - 6

l = 15

So, the required slant height is 15 cm.

Problem 3 :

Solution :

Total surface area = πr(l + r)

πr(l + r) = 60π

5π(l + 5) = 60π

5(l + 5) = 60

Dividing by 5 on both sides.

l + 5 = 12

Subtracting 5 on both sides.

l = 12 - 5

l = 7

So, the required slant height is 7 ft.

Problem 4 :

Solution :

Total surface area = πr(l + r)

πr(l + r) = 216π

9π(l + 9) = 216π

9(l + 9) = 216

Dividing by 9 on both sides.

l + 9 = 24

Subtracting 9 on both sides.

l = 24-9

l = 15

So, the required slant height is 15 cm

Problem 5 :

Solution :

Total surface area = πr(l + r)

πr(l + r) = 792π

11π(x + 11) = 792π

11(x + 11) = 792

Dividing by 11 on both sides.

x + 11 = 72

Subtracting 11 on both sides.

x = 72 - 11

x = 61

So, the required slant height is 61 cm

Problem 6 :

Solution :

Total surface area = πr(l + r)

πr(l + r) = 100π

2π(x + 2) = 100π

2(x + 2) = 50

Dividing by 2 on both sides.

x + 2 = 25

Subtracting 2 on both sides.

x = 25 - 2

x = 23

So, the required slant height is 23 cm.

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