Question

If a semicircle piece of paper of radius 14 cm is rolled to form a cone, then the LSA and radius of cone are​

Answer 1

Given :-

• A semicircle piece of paper of radius 14 cm is rolled to form a cone .

To Find :-

• The LSA of cone.

• The radius of cone.

Solution :-

Case 1 :-

The radius of cone

The Radius of semicircle = 14 cm .......(1)

The Circumference of semicircle = πr ....(2)

Putting value from equation 1 in equation 2 .

Circumference = πr

➝ π × 14

Then, the circumference of base of cone = The circumferance of semicircle.

2πR = 14 π

➝ R = $\cancel{\dfrac{14\pi}{7\pi}}$

➝ R = 7 cm

The r of semi circular sheet is equals to l of conical cup. (l refers to slant hieght)

R = l = 7 cm

l = 7 cm

Case 2 :-

The LSA of cone :-

L.S.A. = π r l

➝ L.S.A. = π × 7 × 7

➝ L.S.A. = $\dfrac{22}{7}$ × 7 × 7

➝ L.S.A. = 22 × 7

➝ L.S.A. = 154

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Answer 2

GIVEN=

• A semicircle piece of paper of radius 14 cm is rolled to form a cone .

TO PROVE=

The LSA of cone.

The radius of cone.

solution=

The radius of cone

The radius of conePutting value from equation 1 in equation 2 .

The radius of conePutting value from equation 1 in equation 2 .Circumference = πr

The radius of conePutting value from equation 1 in equation 2 .Circumference = πr➝ π × 14

2πR = 14 π

2πR = 14 π➝ R = 14π

7π

➝ R = 7 cm

The r of semi circular sheet is equals to l of conical cup. (l refers to slant hieght)

R = l = 7 cm

1=7cm