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RUDIKE [14]
3 years ago
7

Cones A and B both have volume 48(3.14) cubic units but they have different dimensions. Cone A has radius 6 units and height 4 u

nits.
Part A

Find one possible radius and height for Cone B.
Radius: Height:

Part B
Explain how you know Cone B has the same volume as Cone A. ​
Mathematics
1 answer:
OverLord2011 [107]3 years ago
4 0

<u>Part A </u>r =6\sqrt{2}  units & h = 2 units:

<u>Step-by-step explanation:</u>

Here we have , cones A and B both have volume 48(3.14) cubic units but they have different dimensions. Cone A has radius 6 units and height 4 units. We need to find:

Part A

Find one possible radius and height for Cone B.

Since , volume of cone A and B are same so ,

Volume of cone A = V_1 , Volume of cone V = V_2

By hit & trial , One possible radius and height for Cone B is r =6\sqrt{2}  units & h = 2  units:

⇒ V_2 = \frac{1}{3}\pi r^2h

⇒ V_2 = \frac{1}{3}(3.14) (6\sqrt{2})^2(2)

⇒ V_2 = 48units^3

Part B

Explain how you know Cone B has the same volume as Cone A. ​

Volume of cone A = V_1 :

Cone A has radius 6 units and height 4 units, So

⇒ V_1 = \frac{1}{3}\pi r^2h

⇒ V_1 = \frac{1}{3}(3.14) (6})^2(4)

⇒ V_2 = 48units^3

Volume of cone V = V_2

⇒ V_2 = \frac{1}{3}\pi r^2h

⇒ V_2 = \frac{1}{3}(3.14) (6\sqrt{2})^2(2)

⇒ V_2 = 48units^3

Hence, Volume of both are same!

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