Question

N a circular sheet of paper of radius 20 cm, a sector of 30% area is removed and the remaining part is used to make a conical surface. find the approximate volume of the conical surface in cubic cm ( assume √ 51 = 7 )

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer:

The approximate value of volume of the conical surface in cubic cm is 2929.4944 $cm^{3}$

Step-by-step explanation:

Given:

• Circular sheet of paper of radius 20 cm
• 30% area is removed and the remaining part is used to make conical surface.

To find: The approximate value of volume of the conical surface in cubic cm

Solution:

Circumference of circular sheet of paper = 2πr

Given that radius is 20 cm

r = 20

Circumference of circular sheet = 2πr

                                                     =  2π × 20

                                                     = 40 π cm

30% area is removed and the remaining part is used to make conical surface.

Perimeter of base of conical surface  = 40 π × $\frac{(100 - 30)}{100}$

                                                              = 40  π × $\frac{70}{100}$

                                                              = 40  π × $\frac{7}{10}$

                                                               = 4   π  × 7

                                                               = 28 π cm

Radius of base of conical surface = $\frac{28\pi }{2\pi }$

                                                        = 14 cm

Height of the conical surface = $\sqrt{(radius of sheet of paper) ^{2} - (radius of base of conical surface)^{2} }$

= $\sqrt{(20)^{2} - (14)^{2} }$

=$\sqrt{400 - 196}$

= $\sqrt{204}$

≈ 14.28 cm

Volume of conical surface = $\frac{1}{3} \pi r^{2} h$

                                            = $\frac{1}{3} \pi (14)^{2}$× 14.28

                                            ≈ 2929.4944 $cm^{3}$

Final answer:

The approximate value of volume of the conical surface in cubic cm is 2929.4944 $cm^{3}$

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