6.4.10 CYU

Front

What is the volume of a cube with edge length 4 inches?

Back

The volume of a cube is calculated using the formula V = side^3. For a cube with edge length 4 inches, V = 4^3 = 64 cubic inches.

Front

How many little cubes with edge length \( \frac{1}{2} \) inch fit into a larger cube with edge length 4 inches?

Back

To find the number of little cubes, calculate the volume of the larger cube (4^3 = 64 cubic inches) and the volume of one little cube (\( \left(\frac{1}{2}\right)^3 = \frac{1}{8} \) cubic inches). Then, divide the volume of the larger cube by the volume of one little cube: \( 64 \div \frac{1}{8} = 64 \times 8 = 512 \).

Front

What expression can be used to find how many cubes with edge length of \( \frac{1}{3} \) unit fit in a prism that is 5 units by 5 units by 8 units?

Back

The expression is \( (5 \cdot 3) \cdot (5 \cdot 3) \cdot (8 \cdot 3) \). This calculates the number of cubes along each dimension.

Front

What is \( \frac{5}{6} \div \frac{1}{2} \)?

Back

To divide fractions, multiply by the reciprocal: \( \frac{5}{6} \times \frac{2}{1} = \frac{10}{6} = 1\frac{2}{3} \).

Front

What is \( \frac{8}{9} \div \frac{2}{3} \)?

Back

To divide fractions, multiply by the reciprocal: \( \frac{8}{9} \times \frac{3}{2} = \frac{24}{18} = 1\frac{1}{3} \).

Front

What is \( \frac{7}{8} \div \frac{1}{4} \)?

Back

To divide fractions, multiply by the reciprocal: \( \frac{7}{8} \times \frac{4}{1} = \frac{28}{8} = 3\frac{1}{2} \).

Front

Define volume in the context of geometry.

Back

Volume is the amount of space occupied by a three-dimensional object, measured in cubic units.

Front

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

Back

The volume of a rectangular prism is calculated using the formula V = length × width × height.

Front

How do you find the volume of a cube?

Back

The volume of a cube is found using the formula V = side^3, where 'side' is the length of one edge of the cube.

Front

What is the relationship between the edge length of a cube and its volume?

Back

The volume of a cube increases with the cube of its edge length. Doubling the edge length increases the volume by a factor of eight.