Question

what is your answer?

1. use your formula from activity 1 to verify your results in activity 3.

1. in your own words how can you find the surface area of a prism?

1. reasoning when comparing ice blocks with the same volume, the ice with the greater surface area will melt faster. which will melt faster, the bigger block or the three smaller blocks? explain your reasoning.

3 ft
1 ft 1 ft
1 ft
1 ft 1 ft

Explanation:

Step1: Calculate volume of big prism

Volume formula: $V = l \times w \times h$
$V_{big} = 3 \times 1 \times 1 = 3$ ft³

Step2: Calculate surface area of big prism

Surface area formula for rectangular prism: $SA = 2(lw + lh + wh)$
$SA_{big} = 2(3 \times 1 + 3 \times 1 + 1 \times 1) = 2(3 + 3 + 1) = 2 \times 7 = 14$ ft²

Step3: Calculate volume of one small cube

$V_{small} = 1 \times 1 \times 1 = 1$ ft³
Total volume of 3 small cubes: $3 \times 1 = 3$ ft³ (matches big prism)

Step4: Calculate surface area of one small cube

Surface area formula for cube: $SA = 6s^2$
$SA_{one small} = 6 \times 1^2 = 6$ ft²
Total SA of 3 small cubes: $3 \times 6 = 18$ ft²

Step5: Compare surface areas

$18 > 14$, so 3 small blocks have larger SA.

Answer:

(for question 5):
To find the surface area of a prism, first calculate the area of the two identical polygonal bases. Then find the area of each of the rectangular (or parallelogram) lateral faces that connect the corresponding sides of the two bases. Add the total area of the two bases to the total area of all the lateral faces to get the total surface area.