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A cube with an edge of 20 cm is filled with water. Would this amount of water fit in a sphere with a 20 cm radius?

Sagot :

Misspancitcantonidn

Answer:

Yes. The amount of water from the cube would fit in the sphere. In fact, we can still put more water to fill in the sphere.

Step-by-step explanation:

Volume Word Problem

There are three steps to know if the water from the cube would fit in the sphere.

1. Find the volume of the cube.

2. Find the volume of the sphere.

3. Compare their volumes and determine if the water would fit in the sphere.

Let us analyze the given problem above.

Given:

edge of the cube - 20 cm

radius of the sphere - 20 cm

Equation:

Volume of a Cube

V = s³

To find the volume of a cube, we need to multiply its edge, three times by itself.

Volume of a Sphere

V = ‌4⁄3‌πr³

The volume of a sphere is four-thirds times pi times the radius cubed.

Solution:

Step#1: Volume of the Cube

V = s³

= (20 cm)³

= 8000 cm³

The volume of the cube is 8000 cm³.

Step #2: Volume of the Sphere

V = ‌4⁄3‌πr³

= ‌4⁄3‌(3.14)(20 cm)³

= 4⁄3‌(3.14)(8000 cm³)

= 33520 cm³

The volume of the sphere is 33520 cm³.

Step #3: Compare

8000 cm³ < 33520 cm³

Since the cube can hold less amount of water than the sphere, water from it would fit in the sphere.

Final Answer:

Yes. The amount of water from the cube would fit in the sphere. In fact, we can still put more water to fill in the sphere.

For volume word problems, visit the links:

https://brainly.ph/question/105974

https://brainly.ph/question/267431

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