Volume and Surface Area of Solids

This video tutorial from Mumu Math covers the calculation of volumes for various geometric shapes, including prisms, cylinders, pyramids, and cones. It begins with an introduction to the characteristics of these shapes and their volume formulas. The tutorial provides examples of volume calculations for different shapes, including advanced cases like trapezoidal bases. It also explains the relationship between the volumes of prisms, cones, and pyramids, emphasizing the concept of dividing a prism's volume by three to find the volume of a cone or pyramid. The video concludes with a call to practice these calculations.

What is a common characteristic of prisms and cylinders?

• They have a single base.

• They have parallel bases.

• They are two-dimensional.

• They have no height.

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CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

How do you calculate the volume of a cylinder?

• 1/3 of base area times height

• Length times width times height

• Base area times height

• Base area times width

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CCSS.7.G.B.6

What is the formula for the volume of a rectangular prism?

• Length times width times height

• 1/2 base times height

• Pi times radius squared times height

• Base area times height

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CCSS.7.G.B.6

How do you find the volume of a triangular prism?

• Length times width times height

• Pi times radius squared times height

• Base area times height

• 1/2 base times height of the triangle times height of the prism

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CCSS.6.G.A.1

What is the base area formula for a trapezoidal base?

• Base times height

• Length times width

• Pi times radius squared

• 1/2 height times the sum of the bases

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CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

What is the relationship between the volume of a prism and a cone?

• The cone's volume is equal to the prism's volume.

• The cone's volume is one-third the prism's volume.

• The cone's volume is half the prism's volume.

• The cone's volume is twice the prism's volume.

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CCSS.HSG.GMD.A.3

How do you calculate the volume of a pyramid?

• Pi times radius squared times height

• Length times width times height

• 1/3 base area times height

• Base area times height

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CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

What is the formula for the volume of a cone?

• Base area times height

• 1/3 base area times height

• Length times width times height

• Pi times radius squared times height

In a cone, what is the height always perpendicular to?

• The slant height

• The radius

• The base

• The diameter

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CCSS.HSG.GMD.A.3

What is the volume of a pyramid with a base area of 36 and height of 6?

• 72

• 108

• 12

• 216

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CCSS.HSG.GMD.A.3