Question

1. paula designs a character for a video game. she draws three sizes of the character on grid paper. paula uses the expression $6 + s^2$ to find the number of grid squares in a character of any size $s$. find the number of grid squares in a character of size 7. show your work.

1. evaluate the expression $p^3 - q^4 + 3r \div 2$ for $p = 6$, $q = 2$, and $r = 4$. show your work.

1. you can use the formula $a = 6s^2$ to find the surface area of a cube with edge length $s$. a cube has edges that are 10 in. long. what is the surface area of the cube? show your work.

Explanation:

First Problem (Evaluate \( p^3 - q^4 + 3r \div 2 \) for \( p = 6 \), \( q = 2 \), \( r = 4 \))

Step1: Substitute values

Substitute \( p = 6 \), \( q = 2 \), \( r = 4 \) into the expression:
\( 6^3 - 2^4 + 3(4) \div 2 \)

Step2: Calculate exponents

Calculate \( 6^3 = 216 \) and \( 2^4 = 16 \):
\( 216 - 16 + 3(4) \div 2 \)

Step3: Multiply and divide

Calculate \( 3(4) = 12 \), then \( 12 \div 2 = 6 \):
\( 216 - 16 + 6 \)

Step4: Add and subtract

First, \( 216 - 16 = 200 \), then \( 200 + 6 = 206 \):

Second Problem (Surface Area of a Cube with \( s = 10 \) in)

Step1: Identify the formula

The formula for the surface area of a cube is \( A = 6s^2 \), where \( s = 10 \) in.

Step2: Substitute \( s = 10 \)

Substitute \( s = 10 \) into the formula:
\( A = 6(10)^2 \)

Step3: Calculate \( 10^2 \)

\( 10^2 = 100 \), so:
\( A = 6 \times 100 \)

Step4: Multiply

\( 6 \times 100 = 600 \):

First Problem Answer:

\( 206 \)

Second Problem Answer:

\( 600 \) square inches

Answer:

Step1: Identify the formula

The formula for the surface area of a cube is \( A = 6s^2 \), where \( s = 10 \) in.

Step2: Substitute \( s = 10 \)

Substitute \( s = 10 \) into the formula:
\( A = 6(10)^2 \)

Step3: Calculate \( 10^2 \)

\( 10^2 = 100 \), so:
\( A = 6 \times 100 \)

Step4: Multiply

\( 6 \times 100 = 600 \):

First Problem Answer:

\( 206 \)

Second Problem Answer:

\( 600 \) square inches