Change in Dimensions

Front

What is the volume of a cube with a side length of 4 meters?

Back

64 cubic meters (Volume = side³ = 4³ = 64)

Tags

CCSS.5.MD.C.5B

CCSS.6.G.A.2

Front

If a cube's volume is reduced by a scale factor of 1/2, what happens to its side length?

Back

The side length is also reduced by a scale factor of 1/2.

Tags

CCSS.5.MD.C.5B

CCSS.6.G.A.2

Front

What is the relationship between scale factor and volume change in three-dimensional shapes?

Back

Volume changes by the cube of the scale factor (V' = k³ * V).

Tags

CCSS.5.MD.C.5B

CCSS.6.G.A.2

Front

If a solid is enlarged by a scale factor of 2, how does the surface area change?

Back

Surface area changes by the square of the scale factor (A' = k² * A).

Tags

CCSS.7.G.B.6

Front

What is the volume of a cylinder with a radius of 3 inches and a height of 5 inches?

Back

Volume = πr²h = π(3)²(5) = 45π cubic inches.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

Front

If a cylinder's radius is doubled, how does its volume change?

Back

The volume increases by a factor of 8 (2³) because volume depends on the cube of the radius.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

Front

What is the volume of a rectangular prism with dimensions 2m x 3m x 4m?

Back

24 cubic meters (Volume = length × width × height = 2 × 3 × 4 = 24).

Tags

CCSS.7.G.B.6

Front

How do you calculate the volume of a sphere?

Back

Volume = (4/3)πr³.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

Front

If the radius of a sphere is tripled, how does its volume change?

Back

The volume increases by a factor of 27 (3³) because volume depends on the cube of the radius.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

Front

What is the volume of a ball with a radius of 3 inches?

Back

Volume = (4/3)π(3)³ = 36π cubic inches.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3