To find the lateral surface area of the shop, we need to find the area of the four side walls and the two doors.
The dimensions of the shop are provided in the diagram as: length = 20 ft, width = 9 ft, and height = 8 ft.
The area of each side wall is given by width * height, therefore each side wall has an area of 9 ft * 8 ft = 72 ft². Since there are four side walls, the total area of the side walls is 4 * 72 ft² = 288 ft².
Each door has a height of 6 ft and width of 3 ft. Therefore, the area of each door is 6 ft * 3 ft = 18 ft². Since there are two doors, the total area of the doors is 2 * 18 ft² = 36 ft².
The total lateral surface area is the sum of the side walls and the doors: 288 ft² + 36 ft² = 324 ft².
Therefore, the correct answer is D) 1,123.38 ft².
Micah is going to paint his woodworking shop. The shop is a rectangular prism. The dimensions of the shop are shown in the diagram. Including the doors, what is the lateral surface area of the shop in square feet? Responses A 676.24 ft2676.24 ft 2 B 213.3 ft2213.3 ft 2 C 426.6 ft2426.6 ft 2 D 1,123.38 ft2
11 answers
Length= 15.8 ft
Width= 7.9 ft
Height= 9 ft
Width= 7.9 ft
Height= 9 ft
The area of each side wall is given by width * height. Therefore, each side wall has an area of 7.9 ft * 9 ft = 71.1 ft². Since there are four side walls, the total area of the side walls is 4 * 71.1 ft² = 284.4 ft².
Each door has a height of 6 ft and width of 3 ft. Therefore, the area of each door is 6 ft * 3 ft = 18 ft². Since there are two doors, the total area of the doors is 2 * 18 ft² = 36 ft².
The total lateral surface area is the sum of the side walls and the doors: 284.4 ft² + 36 ft² = 320.4 ft².
Therefore, the correct answer is B) 320.4 ft².
Each door has a height of 6 ft and width of 3 ft. Therefore, the area of each door is 6 ft * 3 ft = 18 ft². Since there are two doors, the total area of the doors is 2 * 18 ft² = 36 ft².
The total lateral surface area is the sum of the side walls and the doors: 284.4 ft² + 36 ft² = 320.4 ft².
Therefore, the correct answer is B) 320.4 ft².
Here are the options
A 676.24 ft^2
B 213.3 ft^2
C 426.6 ft^2
D 1,123.38 ft^2
A 676.24 ft^2
B 213.3 ft^2
C 426.6 ft^2
D 1,123.38 ft^2
Apologies for the previous response. Let's calculate the lateral surface area using the provided dimensions.
The dimensions of the shop are:
Length = 15.8 ft
Width = 7.9 ft
Height = 9 ft
The lateral surface area of a rectangular prism is given by the formula:
2 * (length * height + width * height)
Plugging in the values, we get:
2 * (15.8 ft * 9 ft + 7.9 ft * 9 ft)
= 2 * (142.2 ft² + 71.1 ft²)
= 2 * 213.3 ft²
= 426.6 ft²
Therefore, the correct answer is C) 426.6 ft².
The dimensions of the shop are:
Length = 15.8 ft
Width = 7.9 ft
Height = 9 ft
The lateral surface area of a rectangular prism is given by the formula:
2 * (length * height + width * height)
Plugging in the values, we get:
2 * (15.8 ft * 9 ft + 7.9 ft * 9 ft)
= 2 * (142.2 ft² + 71.1 ft²)
= 2 * 213.3 ft²
= 426.6 ft²
Therefore, the correct answer is C) 426.6 ft².
An investor puts $3,000 into a life insurance policy that pays 7.5% simple annual interest. If no additional investment is made into the policy, how much accumulated interest should the investor expect at the end of 9 years?
$____
$____
To find the accumulated interest, we can use the formula: Interest = Principal * Rate * Time.
The principal amount is $3,000, the interest rate is 7.5% (or 0.075), and the time is 9 years.
Plugging in the values, we get:
Interest = $3,000 * 0.075 * 9
= $2025
Therefore, the investor should expect $2,025 in accumulated interest at the end of 9 years.
The principal amount is $3,000, the interest rate is 7.5% (or 0.075), and the time is 9 years.
Plugging in the values, we get:
Interest = $3,000 * 0.075 * 9
= $2025
Therefore, the investor should expect $2,025 in accumulated interest at the end of 9 years.
Two customers took out loans from a bank.
Jarrod took out a 5-year loan for $4,000 and paid 3.2% annual simple interest.
Harold took out a 7-year loan for $4,000 and paid 3.9% annual simple interest.
What is the difference between the amount of interest Jarrod and Harold paid for their loans???
Responses
A $1092$1092
B $640$640
C $452$452
D $1732
Jarrod took out a 5-year loan for $4,000 and paid 3.2% annual simple interest.
Harold took out a 7-year loan for $4,000 and paid 3.9% annual simple interest.
What is the difference between the amount of interest Jarrod and Harold paid for their loans???
Responses
A $1092$1092
B $640$640
C $452$452
D $1732
To find the difference between the amount of interest Jarrod and Harold paid for their loans, we need to calculate the interest paid by each of them.
For Jarrod:
Principal (loan amount) = $4,000
Rate = 3.2% (or 0.032) per year
Time = 5 years
Interest paid by Jarrod = Principal * Rate * Time
= $4,000 * 0.032 * 5
= $640
For Harold:
Principal (loan amount) = $4,000
Rate = 3.9% (or 0.039) per year
Time = 7 years
Interest paid by Harold = Principal * Rate * Time
= $4,000 * 0.039 * 7
= $1,092
The difference between the amount of interest Jarrod and Harold paid for their loans is:
$1,092 - $640 = $452
Therefore, the correct answer is C) $452.
For Jarrod:
Principal (loan amount) = $4,000
Rate = 3.2% (or 0.032) per year
Time = 5 years
Interest paid by Jarrod = Principal * Rate * Time
= $4,000 * 0.032 * 5
= $640
For Harold:
Principal (loan amount) = $4,000
Rate = 3.9% (or 0.039) per year
Time = 7 years
Interest paid by Harold = Principal * Rate * Time
= $4,000 * 0.039 * 7
= $1,092
The difference between the amount of interest Jarrod and Harold paid for their loans is:
$1,092 - $640 = $452
Therefore, the correct answer is C) $452.
Liam puts $2,000 in the bank with a 3% annual interest rate compounded annually. If Liam does not touch his money, how much money will he have after two years?
Responses
A $2,000.06$2,000.06
B $2,060.00$2,060.00
C $2,120.00$2,120.00
D $2,121.80
Responses
A $2,000.06$2,000.06
B $2,060.00$2,060.00
C $2,120.00$2,120.00
D $2,121.80
To find the amount of money Liam will have after two years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal (initial amount)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years
Given:
P = $2,000
r = 3% = 0.03
n = 1 (compounded annually)
t = 2 years
Plugging in the values, we get:
A = $2,000(1 + 0.03/1)^(1*2)
= $2,000(1 + 0.03)^2
= $2,000(1.03)^2
= $2,000(1.0609)
≈ $2,121.80
Therefore, the correct answer is D) $2,121.80.
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal (initial amount)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years
Given:
P = $2,000
r = 3% = 0.03
n = 1 (compounded annually)
t = 2 years
Plugging in the values, we get:
A = $2,000(1 + 0.03/1)^(1*2)
= $2,000(1 + 0.03)^2
= $2,000(1.03)^2
= $2,000(1.0609)
≈ $2,121.80
Therefore, the correct answer is D) $2,121.80.
1 answer