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The formula for finding the volume of a square prism is s2h , where s is the length of each side of the square base and h is the height of the prism. Evaluate to find the volume given values of s = 4 and h = 6 .(1 point)

Responses

576 cubic centimeters
576 cubic centimeters

96 cubic centimeters
96 cubic centimeters

144 cubic centimeters
144 cubic centimeters

48 cubic centimeters

7 answers

To find the volume of a square prism using the formula \( V = s^2 h \), where \( s \) is the length of each side of the square base and \( h \) is the height, we can plug in the values given:

  • \( s = 4 \) cm
  • \( h = 6 \) cm

Now, let's calculate:

  1. First, calculate \( s^2 \): \[ s^2 = 4^2 = 16 \text{ cm}^2 \]

  2. Next, multiply by the height \( h \): \[ V = s^2 h = 16 \text{ cm}^2 \times 6 \text{ cm} = 96 \text{ cm}^3 \]

The volume of the square prism is \( 96 \) cubic centimeters.

The correct response is: 96 cubic centimeters.

Each month Ms. Tanaka is paid a base salary of $2,500 in addition to $100 for each television that she sells. This is modeled by 2,500 + 100t , where t represents the number of televisions. Evaluate for t = 12 to find how much Ms. Tanaka will earn for selling 12 televisions this month.(1 point)
Responses

$31,200
$31,200

$2,612
$2,612

$2,600
$2,600

$3,700

To find out how much Ms. Tanaka will earn for selling 12 televisions, we can use the formula:

\[ \text{Total Earnings} = 2500 + 100t \]

where \( t \) is the number of televisions sold. Given \( t = 12 \), we can substitute this value into the formula:

\[ \text{Total Earnings} = 2500 + 100(12) \] \[ = 2500 + 1200 \] \[ = 3700 \]

Therefore, Ms. Tanaka will earn $3,700 this month for selling 12 televisions.

The correct response is: $3,700.

Robert is preparing a poster-board presentation. He wants to make a decorative pattern with 10 squares to fill part of the poster. The area of the poster board is 720 square inches. To find how much space Robert will have left for his presentation if he uses squares with 7-inch sides, evaluate 720 − 10s2 when s = 7.(1 point)
Responses

580 square inches
580 square inches

34,790 square inches
34,790 square inches

9,940 square inches
9,940 square inches

230 square inches

To find out how much space Robert will have left for his presentation after filling part of the poster with squares, we first need to calculate the area taken up by the 10 squares, where each square has a side length of \( s = 7 \) inches.

  1. First, calculate the area of one square: \[ \text{Area of one square} = s^2 = 7^2 = 49 \text{ square inches} \]

  2. Then calculate the total area for 10 squares: \[ \text{Total area of 10 squares} = 10 \times 49 = 490 \text{ square inches} \]

  3. Next, subtract the total area of the squares from the area of the poster board: \[ \text{Space left} = 720 - (\text{Total area of squares}) \] \[ \text{Space left} = 720 - 490 = 230 \text{ square inches} \]

Therefore, the space Robert will have left for his presentation is 230 square inches.

The correct response is: 230 square inches.

Mr. Rodriguez has a vegetable garden that borders his house. He wants to put a fence around it. It costs $7 per yard for the materials. Evaluate 7(l + 2w), where l is the length and w is the width of his garden, to find the cost for a garden that has a length of 5 yards and a width of 2 yards.(1 point)
Responses

$63
$63

$39
$39

$98
$98

$16

To find the cost to fence Mr. Rodriguez's vegetable garden, we will evaluate the expression \( 7(l + 2w) \), where:

  • \( l \) is the length of the garden (5 yards)
  • \( w \) is the width of the garden (2 yards)

Let's substitute these values into the expression:

  1. Substitute \( l \) and \( w \): \[ 7(l + 2w) = 7(5 + 2 \times 2) \]

  2. Calculate \( 2w \): \[ 2w = 2 \times 2 = 4 \]

  3. Now substitute back into the expression: \[ 7(5 + 4) = 7(9) \]

  4. Finally, multiply by 7: \[ 7 \times 9 = 63 \]

Therefore, the cost to put a fence around the garden is $63.

The correct response is: $63.