High School

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28) The volume of a cylinder is 38.5 cubic centimeters and the height is 6 centimeters. What is the area of the

base circle? Round the answer to the nearest hundredth. (Hint: Work backwards.)

B=?cm²

V=38.5 cm'

h=6cm

28 The volume of a cylinder is 38 5 cubic centimeters and the height is 6 centimeters What is the area of the base circle

Answer :

Answer :

  • Area of base circle = 6.42 cm²

Step-by-step explanation:

Given :-

  • Volume of cylinder = 38.5 cu cm.
  • Height of cylinder = 6 cm.

To Find :-

  • Area of base?

Solution :-

We know,

  • Area of Base = πr².

In order to calculate to Area of base firstly we need to calculate the radius of the cylinder.

We are provided with Volume of cylinder that is 38.5 cm³.

We know,

  • Volume of cylinder = πr²h

[tex] \: :\implies [/tex] 3.14 × r² × 6 = 38.5

[tex] \: :\implies [/tex] 18.84 × r² = 38.5

[tex] \: :\implies [/tex] 2.04 3

[tex] \: :\implies [/tex] 1.4292

[tex] \: :\implies [/tex] 1.43 (nearest hundredth)

Radius of the cylinder is 1.43 cm.

Now,

  • Area of base = πr²

[tex] \: :\implies [/tex] 3.14 × (1.43)²

[tex] \: :\implies [/tex] 3.14 × 2.0449

[tex] \: :\implies [/tex] 6.420986

[tex] \: :\implies [/tex] 6.42 (nearest hundredth)

Therefore, Area of the base circle is 6.42cm².

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