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If a cone-shaped vase can hold 45 cubic centimeters of water and has a radius of 2 centimeters, what is the height of the vase? Use 3.14 for pi. Round your answer to the nearest hundredth.


7.45 centimeters

10.75 centimeters

14.33 centimeters

22.50 centimeters

Verified Answer :

volume of a cone  V = pi r r h / 3
so V = 45, r = 2 therefore 45 = 3.14 2 2 h /3  => 45 = 3.14 4 h /3
=> 135 = 3.14 4 h  => 33.75 = 3.14 * h  => 10.75 = h
height = 10.75 cm rounded to 2 decimal places

Answer:

The height of the cone is 10.75 cm.

Step-by-step explanation:

Given the volume of cone = 45 cubic cm

Radius of the cone = 2 cm

Height of the cone = ?

The volume formula of cone is = \(\pi r^{2} \frac{h}{3}\)

\(45= 3.14\times2\times2\times \frac{h}{3}\)

=> \(45\times3 =12.56h\)

=> \(135=12.56h\)

h = 10.748 ≈ 10.75 cm

So, the height of the cone is 10.75 cm.

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