Composite Solids & Changing Dimensions

Front

What is a composite solid?

Back

A composite solid is a three-dimensional shape that is made up of two or more simple geometric shapes.

Tags

CCSS.1.G.A.2

Front

How do you find the volume of a prism?

Back

The volume of a prism is found by multiplying the area of the base by the height of the prism (Volume = Base Area × Height).

Tags

CCSS.7.G.B.6

Front

What happens to the volume of a prism if all dimensions are reduced by a factor of 1/3?

Back

If all dimensions are reduced by a factor of 1/3, the new volume is reduced by a factor of (1/3)³, which is 1/27 of the original volume.

Front

If the volume of a prism is 80 in³, what is the volume if each edge is halved?

Back

The new volume will be 10 in³, as halving each dimension reduces the volume to 1/8 of the original (80 in³ ÷ 8 = 10 in³).

Front

What is the formula for the volume of a cylinder?

Back

The volume of a cylinder is calculated using the formula: Volume = π × r² × h, where r is the radius and h is the height.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

Front

What is the relationship between the dimensions of a solid and its volume?

Back

The volume of a solid is directly related to its dimensions; changing any dimension will affect the overall volume.

Tags

CCSS.5.MD.C.3A

CCSS.5.MD.C.3B

CCSS.5.MD.C.4

Front

How do you calculate the volume of a rectangular prism?

Back

The volume of a rectangular prism is calculated by multiplying its length, width, and height (Volume = Length × Width × Height).

Tags

CCSS.7.G.B.6

Front

What is the effect of doubling the dimensions of a prism on its volume?

Back

Doubling the dimensions of a prism increases its volume by a factor of 2³, which is 8 times the original volume.

Tags

CCSS.7.G.B.6

Front

What is the volume of a prism with a base area of 20 cm² and a height of 5 cm?

Back

The volume is 100 cm³, calculated as Volume = Base Area × Height (20 cm² × 5 cm = 100 cm³).

Tags

CCSS.7.G.B.6

Front

If a prism has a volume of 200 cm³ and its height is doubled, what happens to the volume?

Back

The volume will also double, resulting in a new volume of 400 cm³.

Tags

CCSS.7.G.B.6