Question

maths legend please help please

Answer 1

In the first figure :-

Given that :-

Height (OP) = 2 cm
Radius (OB) 3.5 cm

Slant Height (PB) ^2= OP^2 + OB^2

$= > l \: = \: \sqrt{ {2}^{2} + {3.5}^{2} }$

$= > \: l \: = \sqrt{16.25}$

$= > \: l \: = 4.03$


Now,

$= > \: c.s.a \: = \pi \: r \: l \:$

=> C.S.A = 22/7 x 3.5 x 4.03

=> C.S.A = 44.33 cm^2

Now,

Second Figure,

Height = 3.5 cm

Diameter = 10 cm

Radius = 10/2 cm = 5 cm

Slant Height^2 = Height^2 + Radius^2

$= > \: l \: = \sqrt{ {3.5}^{2} + {5}^{2} }$

$= > \: l \: = \sqrt{37.25} = 6.10 \: cm$
$= > \: c.s.a \: = \pi \: r \: l \:$
=> C.S.A = 22/7 x 5 x 6.10

=> C.S.A = 95.85 cm^2

Since, In Cone both C.S.A and T.S.A are equal to eachother.



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Answer 2

Answer:

1 ) When the right angle triangles are revolved in such manner, two right circular cones are formed with different radius and heights.

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2 )

Case 1 : Cone with Radius 3.5 cm and Height 2 cm

CSA of Cone = πrl

⇒ l = √ ( h² + r² )

⇒ l = √ ( 2² + 3.5² )

⇒ l = √ ( 4 + 12.25 )

⇒ l = √ 16.25 = 4.03 cm

Hence CSA ⇒ 3.14 × 2 × 4.03 = 25.3084 cm²

TSA of Cone = πrl + Area of Base

⇒ Area of base = πr² ⇒ 3.14 × 2² = 3.14 × 4 = 12.56 cm²

⇒ TSA of cone = 25.3084 + 12.5600 = 37.8684 cm²

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Case 2: Cone with diameter 10 cm and height 3.5 cm

Radius = Diameter / 2 = 10 / 2 = 5 cm

CSA = πrl

⇒ l = √ r² + h²

⇒ l = √ 5² + 3.5²

⇒ l = √ 25 + 12.25

⇒ l = √ 37.25 = 6.10 cm

⇒ CSA = 3.14 × 5 × 6.10 = 95.77 cm²

TSA = πrl + Area of Base

Area of Base = πr² = 3.14 × 5² = 3.14 × 25 = 78.5 cm²

⇒ TSA of cone = 78.50 + 95.77 = 174.27 cm²

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These are the required answers !!

Hope it helped !!