For the right circular cone whose base area is 36π cm², the radius of the circular upper surface is 3 cm and the slant height is 5 cm, then what will be the lateral surface area of the frustum of the right circular cone?

LaGiven:

Base Area = 36π cm²

The radius of the circular upper surface, r = 3 cm.

The slant height, l = 5 cm

Formula used:

The lateral surface area of frustum = (πRL - πrl)

Calculation:

Base, Area = 36π 

⇒ πR² = 36π 

⇒ R = √ 36 = 6 cm

Given r = 3 cm

∵ ΔABC ≅ ΔADE

\(BC\over DE\) = \(AC\over AE\)

⇒ \(6\over12\) = \(5\over AE\)

⇒​ AE = 10 cm = L

The lateral surface area of the frustum

⇒ πRL - πrl

⇒ π × 6 × 10 - π × 3 × 5

⇒ 60π - 15π = 45π  

Shortcut Trick Formula Used:

Lateral Surface Area of a Frustum = π (R + r) × l

where,

R & r are the radii of a cone 

L is the slant height

Calculation:

Using the formula, 

⇒ π (6 + 3) × 5

⇒ π (9) × 5

⇒ 45 π 

∴ The lateral surface area of a frustum is 45π.