Question

Surface area of a cone is 188.4 sq.cm and its slant height is 10cm. Find its perpendicular height (π = 3.14)​

Answer 1

Step-by-step explanation:

Given: Surface area of cone (SA) = 188.4 cm2

Slant height of cone (l) = 10 cm

So, we need to write the formula of curved surface area of cone with slant height l,

Surface Area = πrl

Where, r = radius of base of cone

Substituting values in the formula, we get

188.4 = 3.14×r×10

⇒ 188.4 = 31.4r

⇒ r = 188.4/31.4

⇒ r = 6

So we have,

We need to find the perpendicular height, h.

Using Pythagoras theorem in ∆AOB, we get

AB2 = AO2 + OB2

⇒ AO2 = AB2 – OB2

⇒ h2 = 102 – 62

⇒ h2 = 100 – 36 = 64

⇒ h = √64 = 8

Thus, perpendicular height of the cone is 8 cm.

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Answer 2

Step-by-step explanation:

Solution :

Dimensions of the cone :

i ) Slant height ( l ) = 10 cm

Let the height = h cm

Radius = r cm

Surface area of the cone = 188.4 sqcm

=> πrl = 188.4

=> r = 188.4 /( πl )

=> r = 188.4/( 3.14 × 10 )

r = 6 cm

ii ) r = 6 cm , l = 10 cm , h = ?

h² = l² - r²

=> h² = 10² - 6²

=> h² = 100 - 36

=> h² = 64

h = √64

h = 8 cm

Therefore ,

Perpendicular height of the

cone = h = 8 cm

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