Leigh Ann is designing a wrapper for a new dark chocolate candy bar that her company is going to sell. The candy bar is a
triangular prism. The dimensions of the candy bar are shown in the diagram.
G
E
[
7.4 cm
6.9 cm
7.4 cm
9.9 cm
5.1 cm
Which measurement is closest to the total surface area of the candy bar in square centimeters?
Answers: 232.20 197.01 265.32 174.19
To calculate the total surface area of the triangular prism candy bar, we need to find the areas of all the individual faces and then sum them up.
We have three rectangular faces and two triangular faces.
The three rectangular faces:
- The front and back faces have dimensions 7.4 cm by 6.9 cm, so their total area is 2 * (7.4 * 6.9) = 101.64 cm^2.
- The side face has dimensions 9.9 cm by 5.1 cm, so its area is 9.9 * 5.1 = 50.49 cm^2.
The two triangular faces are identical and have a base of 6.9 cm and a height of 7.4 cm. The area of one triangular face is (1/2) * 6.9 * 7.4 = 25.47 cm^2. Since there are two identical triangular faces, their total area is 2 * 25.47 = 50.94 cm^2.
Finally, we add up all the areas:
101.64 + 50.49 + 50.94 = 203.07 cm^2.
The measurement that is closest to the total surface area of the candy bar is 203.07 cm^2. Therefore, the closest answer is 197.01.
Luke deposits $3,500 into each of two savings accounts.
• Account I earns 3% annual simple interest.
• Account II earns 3% interest compounded annually.Luke does not make any additional deposits or withdrawals. What is the sum of the balances of Account I and Account II at the end of 4 years?
Answers:
7,859.28
3,9200.00
3,939.28
4,359.28
To calculate the balance of Account I after 4 years at 3% simple interest, we can use the formula:
Balance = Principal + (Principal * Rate * Time)
Account I:
Principal = $3,500
Rate = 3% = 0.03
Time = 4 years
Balance of Account I = $3,500 + ($3,500 * 0.03 * 4) = $3,500 + $420 = $3,920
To calculate the balance of Account II after 4 years at 3% interest compounded annually, we can use the formula:
Balance = Principal * (1 + Rate)^Time
Account II:
Principal = $3,500
Rate = 3% = 0.03
Time = 4 years
Balance of Account II = $3,500 * (1 + 0.03)^4 = $3,500 * (1.03)^4 = $3,500 * 1.1255 = $3,939.28
The sum of the balances of Account I and Account II at the end of 4 years is:
$3,920 + $3,939.28 = $7,859.28
Therefore, the answer is $7,859.28.