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In the solid pictured, the cylinder has a radius of 4 cm and a height of 10 cm. There is a hole in the cylinder in the shape of a square prism. The base of the prism has side lengths 4 cm.

Calculate the volume of the solid. Round your answer to the nearest tenth.

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In The Solid Pictured The Cylinder Has A Radius Of 4 Cm And A Height Of 10 Cm There Is A Hole In The Cylinder In The Shape Of A Square Prism The Base Of The Pri class=

Sagot :

Answer:

342.7 cubic cm

Step-by-step explanation:

see image

Calculate the volumes of the cylinder and the prism. Subtract.

see image.

View image lpina68

Volume is the amount of three-dimensional space enclosed by a closed surface. The volume of the solid is 342.655 cm³.

What is volume?

The amount of three-dimensional space enclosed by a closed surface is expressed as a scalar quantity called volume.

  • The volume of Cylinder = πr²h
  • The volume of Prism = Area of prism × h

The volume of the solid is the difference between the volume of the cylinder and the volume of the square prism.

[tex]\text{Volume of the solid} =\text{Volume of the cylinder}-\text{Volume of the square prism}[/tex]

[tex]\text{Volume of the solid} =(\pi r^2 h)-(a^2 h)[/tex]

We know that the radius of the cylinder is 4 cm while the length of the side of the square prism is 4 and the height of both is 10cm. therefore, substituting the values,

[tex]\text{Volume of the solid} =(\pi\times 4^2 \times 10)-(4^2 \times 10)[/tex]

                               [tex]=4^2\times10 (\pi -1)\\\\= 342.655\RM\ cm^3[/tex]

Hence, the volume of the solid is 342.655 cm³.

Learn more about Volume:

https://brainly.com/question/1578538

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