Question

Han has 10 cubes, each 5 inches on a side. A) Find the total volume of Han’s cubes. Express your answer as an expression using an exponent. B) Find the total surface area of Han’s cubes. Express your answer as an expression using an exponent.

Answer 1

The total volume of Han's cubes is given by the expression 10 × 5³ cubic inches, and the total surface area can be expressed as 10 × 6 × 5² square inches.

Step-by-step explanation:

The question asks for the calculation of volume and surface area of cubes with a given side length.

Volume Calculation

To find the volume of a single cube, we use the formula V = s³, where s is the length of a side of the cube. Because each side of the cube is 5 inches, the volume of one cube is V = 5³ inches³, which equals 125 cubic inches. Now, Han has 10 cubes, so the total volume is 10 times the volume of one cube, which can be expressed as:

Total Volume = 10 × 5³ inches³

Surface Area Calculation

The surface area of a single cube is found using the formula SA = 6s², since there are six sides to a cube. With a side length of 5 inches, the surface area of one cube is SA = 6 × 5² square inches, which equals 150 square inches. For 10 cubes, the total surface area is 10 times the surface area of one cube, which can be expressed as:

Total Surface Area = 10 × 6 × 5² square inches

Answer 2

A) Vol_10_cubes = 2*(5^4) inch^3

B) Area_10_cubes = (2^2)*3*(5^3) inch^2

Step-by-step explanation:

A)The volume of a cube, as all sides are equal:

Vol_cube = (side)^3

side = 5 inches

Vol_cube = 5^3 inch^3

Since we have 10 cubes

10 = 2*5

Vol_10_cubes = 2*(5^4) inch^3

B) A cube has six faces, each with area equal to its squared side

Area_cube = 6*(side)^2

Area_cube = 6*(5)^2 inch^2

Area_10_cubes = 2*5*6*(5)^2 inch^2

Area_10_cubes = (2^2)*3*(5)^3 inch^2