The radii of the circular ends of a frustum of height 6 cm are 14 cm and 6 cm respectively. Find the slant height of the frustum.
Given height of frustum = h =6 cm
Radius of top = r = 6 cm
Radius of bottom = R = 14 cm
Let the slant height of the frustum be ‘ℓ’ cm
We know in frustum
(Slant height)2 = (height)2 + (R – r)2→eqn1
⇒ ℓ2 = 62 + (14 – 6)2 (putting values of r, R and h in eqn1)
⇒ ℓ2 = 36 + 82
⇒ ℓ2 = 36 + 64
⇒ ℓ2 = 100
⇒ ℓ = √100
∴ ℓ = 10 cm
Slant height of the frustum is 10 cm.
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