To find the amount of glass needed to enclose the aquarium, we need to calculate the surface area of the aquarium.
The aquarium has 6 sides:
- 2 sides that are 17 inches long by 11 inches tall (top and bottom): 17 inches * 11 inches * 2 = 374 square inches
- 2 sides that are 9 inches wide by 11 inches tall (front and back): 9 inches * 11 inches * 2 = 198 square inches
- 2 sides that are 17 inches long by 9 inches wide (sides): 17 inches * 9 inches * 2 = 306 square inches
Total surface area = 374 + 198 + 306 = 878 square inches
Therefore, Tommy and Cole would need to buy 878 square inches of glass to enclose the aquarium.
Tommy and Cole are planning to build an aquarium for their pet fish. If the dimensions of the aquarium
are 17 inches long, 9 inches wide, and 11 inches tall, how much glass do they need to buy to enclose
the aquarium?(1 point)
11 answers
5cm tall 5cm wide 5 cm long
Manny created a storage bin for the family to hold the remote control and cell phone cords. What is
the total surface area of the storage bin?
Manny created a storage bin for the family to hold the remote control and cell phone cords. What is
the total surface area of the storage bin?
To find the total surface area of the storage bin, we need to calculate the surface area of all six sides.
The storage bin has 6 sides:
- 2 sides that are 5 cm long by 5 cm wide: 5 cm * 5 cm * 2 = 50 square cm
- 2 sides that are 5 cm long by 5 cm tall: 5 cm * 5 cm * 2 = 50 square cm
- 2 sides that are 5 cm wide by 5 cm tall: 5 cm * 5 cm * 2 = 50 square cm
Total surface area = 50 + 50 + 50 = 150 square cm
Therefore, the total surface area of the storage bin Manny created is 150 square cm.
The storage bin has 6 sides:
- 2 sides that are 5 cm long by 5 cm wide: 5 cm * 5 cm * 2 = 50 square cm
- 2 sides that are 5 cm long by 5 cm tall: 5 cm * 5 cm * 2 = 50 square cm
- 2 sides that are 5 cm wide by 5 cm tall: 5 cm * 5 cm * 2 = 50 square cm
Total surface area = 50 + 50 + 50 = 150 square cm
Therefore, the total surface area of the storage bin Manny created is 150 square cm.
For Monica’s 14th birthday, she wants to make over her bedroom. The first phase in the bedroom
makeover is painting her room. If Monica’s room is 20 ft. long, 15 ft. wide, and 9 ft. high, find the
surface area of the room that you are going to paint, including the floor and ceiling(1 point)
makeover is painting her room. If Monica’s room is 20 ft. long, 15 ft. wide, and 9 ft. high, find the
surface area of the room that you are going to paint, including the floor and ceiling(1 point)
To find the surface area of Monica's room that needs to be painted, including the floor and ceiling, we will calculate the surface area of all six sides.
Monica's room has 6 sides:
- 2 sides that are 20 ft. long by 9 ft. high (front and back): 20 ft. * 9 ft. * 2 = 360 square ft
- 2 sides that are 15 ft. wide by 9 ft. high (left and right): 15 ft. * 9 ft. * 2 = 270 square ft
- 1 side that is 20 ft. long by 15 ft. wide (floor): 20 ft. * 15 ft. = 300 square ft
- 1 side that is 20 ft. long by 15 ft. wide (ceiling): 20 ft. * 15 ft. = 300 square ft
Total surface area to be painted = 360 + 270 + 300 + 300 = 1230 square ft
Therefore, the surface area of Monica's room that needs to be painted, including the floor and ceiling, is 1230 square ft.
Monica's room has 6 sides:
- 2 sides that are 20 ft. long by 9 ft. high (front and back): 20 ft. * 9 ft. * 2 = 360 square ft
- 2 sides that are 15 ft. wide by 9 ft. high (left and right): 15 ft. * 9 ft. * 2 = 270 square ft
- 1 side that is 20 ft. long by 15 ft. wide (floor): 20 ft. * 15 ft. = 300 square ft
- 1 side that is 20 ft. long by 15 ft. wide (ceiling): 20 ft. * 15 ft. = 300 square ft
Total surface area to be painted = 360 + 270 + 300 + 300 = 1230 square ft
Therefore, the surface area of Monica's room that needs to be painted, including the floor and ceiling, is 1230 square ft.
Christian collects model cars and planes. He has a display showcase of all of his collectors' items.
Solve this real-world problem to find the surface area of the display showcase if it is the shape of a
triangular prism with the following dimensions: h=9 inches, b=17 inches, s1=10 inches, s2=12 inches, s3 17 and l=10 inches
Solve this real-world problem to find the surface area of the display showcase if it is the shape of a
triangular prism with the following dimensions: h=9 inches, b=17 inches, s1=10 inches, s2=12 inches, s3 17 and l=10 inches
To find the surface area of the triangular prism display showcase, we first need to calculate the area of each face of the prism and then add them up.
1. Area of the triangular base:
The base of the triangular prism is a triangle with sides s1, s2, and s3.
Using Heron's formula, we can calculate the area of the base triangle:
s = (s1 + s2 + s3) / 2
area_base = √[s * (s - s1) * (s - s2) * (s - s3)]
where s is the semi-perimeter of the triangle.
s = (10 + 12 + 17) / 2 = 39 / 2 = 19.5
area_base = √[19.5 * (19.5 - 10) * (19.5 - 12) * (19.5 - 17)]
area_base = √[19.5 * 9.5 * 7.5 * 2.5]
area_base = √3447.1875
area_base ≈ 58.665 square inches
2. Area of one lateral face:
The lateral faces of the triangular prism are rectangles. In a triangular prism, a lateral face has the same perimeter as the base triangle.
The area of a rectangle is length multiplied by width.
lateral_area = l * h
lateral_area = 10 * 9
lateral_area = 90 square inches
3. Total surface area:
Each triangular prism has 2 triangular bases (front and back) and 3 lateral faces.
Total surface area = 2 * area_base + 3 * lateral_area
Total surface area = 2 * 58.665 + 3 * 90
Total surface area = 117.33 + 270
Total surface area = 387.33 square inches
Therefore, the surface area of Christian's triangular prism display showcase is approximately 387.33 square inches.
1. Area of the triangular base:
The base of the triangular prism is a triangle with sides s1, s2, and s3.
Using Heron's formula, we can calculate the area of the base triangle:
s = (s1 + s2 + s3) / 2
area_base = √[s * (s - s1) * (s - s2) * (s - s3)]
where s is the semi-perimeter of the triangle.
s = (10 + 12 + 17) / 2 = 39 / 2 = 19.5
area_base = √[19.5 * (19.5 - 10) * (19.5 - 12) * (19.5 - 17)]
area_base = √[19.5 * 9.5 * 7.5 * 2.5]
area_base = √3447.1875
area_base ≈ 58.665 square inches
2. Area of one lateral face:
The lateral faces of the triangular prism are rectangles. In a triangular prism, a lateral face has the same perimeter as the base triangle.
The area of a rectangle is length multiplied by width.
lateral_area = l * h
lateral_area = 10 * 9
lateral_area = 90 square inches
3. Total surface area:
Each triangular prism has 2 triangular bases (front and back) and 3 lateral faces.
Total surface area = 2 * area_base + 3 * lateral_area
Total surface area = 2 * 58.665 + 3 * 90
Total surface area = 117.33 + 270
Total surface area = 387.33 square inches
Therefore, the surface area of Christian's triangular prism display showcase is approximately 387.33 square inches.
Christian collects model cars and planes. He has a display showcase of all of his collectors' items.
Solve this real-world problem to find the surface area of the display showcase if it is the shape of a
triangular prism with the following dimensions: h=9 inches, b=17 inches, s=10 inches, s2=12 inches, s3 17 and l=10 inches
S.A.=________ in.2
Solve this real-world problem to find the surface area of the display showcase if it is the shape of a
triangular prism with the following dimensions: h=9 inches, b=17 inches, s=10 inches, s2=12 inches, s3 17 and l=10 inches
S.A.=________ in.2
Given:
Height (h) = 9 inches
Base side (b) = 17 inches
Side 1 (s1) = 10 inches
Side 2 (s2) = 12 inches
Side 3 (s3) = 17 inches
Length (l) = 10 inches
To find the surface area of the triangular prism display showcase, we can break down the calculations into finding the area of the base triangle and the lateral faces.
1. Area of the base triangle:
Calculate the semi-perimeter:
s = (s1 + s2 + s3) / 2
s = (10 + 12 + 17) / 2
s = 39 / 2
s = 19.5
Use Heron's formula to find the area of the base triangle:
area_base = √[s * (s - s1) * (s - s2) * (s - s3)]
area_base = √[19.5 * (19.5 - 10) * (19.5 - 12) * (19.5 - 17)]
area_base = √[19.5 * 9.5 * 7.5 * 2.5]
area_base = √3440.625
area_base ≈ 58.636 square inches
2. Area of each lateral face:
The lateral faces are rectangles, so the area of a lateral face can be calculated as the product of the length (l) and height (h):
lateral_area = l * h
lateral_area = 10 * 9
lateral_area = 90 square inches
3. Total surface area:
Total surface area = 2 * area_base + 3 * lateral_area
Total surface area = 2 * 58.636 + 3 * 90
Total surface area = 117.272 + 270
Total surface area = 387.272 square inches
Therefore, the surface area of Christian's triangular prism display showcase is approximately 387.272 square inches.
Height (h) = 9 inches
Base side (b) = 17 inches
Side 1 (s1) = 10 inches
Side 2 (s2) = 12 inches
Side 3 (s3) = 17 inches
Length (l) = 10 inches
To find the surface area of the triangular prism display showcase, we can break down the calculations into finding the area of the base triangle and the lateral faces.
1. Area of the base triangle:
Calculate the semi-perimeter:
s = (s1 + s2 + s3) / 2
s = (10 + 12 + 17) / 2
s = 39 / 2
s = 19.5
Use Heron's formula to find the area of the base triangle:
area_base = √[s * (s - s1) * (s - s2) * (s - s3)]
area_base = √[19.5 * (19.5 - 10) * (19.5 - 12) * (19.5 - 17)]
area_base = √[19.5 * 9.5 * 7.5 * 2.5]
area_base = √3440.625
area_base ≈ 58.636 square inches
2. Area of each lateral face:
The lateral faces are rectangles, so the area of a lateral face can be calculated as the product of the length (l) and height (h):
lateral_area = l * h
lateral_area = 10 * 9
lateral_area = 90 square inches
3. Total surface area:
Total surface area = 2 * area_base + 3 * lateral_area
Total surface area = 2 * 58.636 + 3 * 90
Total surface area = 117.272 + 270
Total surface area = 387.272 square inches
Therefore, the surface area of Christian's triangular prism display showcase is approximately 387.272 square inches.
6 in. tall 8 in. long 19 in. wide 10 in. long triangle side
The diagram represents a model of a ramp the skateboard club wants to create at the neighborhood
skate park. If one pint of paint covers 200 square inches, how many pints of paint will the club need to
purchase? Paint is only sold in whole pints.
The diagram represents a model of a ramp the skateboard club wants to create at the neighborhood
skate park. If one pint of paint covers 200 square inches, how many pints of paint will the club need to
purchase? Paint is only sold in whole pints.
To find the total surface area that needs to be painted on the ramp model, we need to calculate the surface area of each face of the ramp.
Given:
- Height (h) = 6 inches
- Long side of the triangle (b) = 10 inches
- Base of the triangle (given it's half the base of the parallelogram) = 8 inches
- Width (w) = 19 inches
First, we will calculate the area of the triangle face:
Area of a triangle = 0.5 * base * height
Area of the triangle face = 0.5 * 8 * 6 = 24 square inches
Next, we will calculate the area of the parallelogram face:
Area of a parallelogram = base * height
Area of the parallelogram face = 10 * 6 = 60 square inches
Now, calculate the area of the rectangle face:
Area of a rectangle = length * width
Area of the rectangle face = 10 * 19 = 190 square inches
Total surface area to be painted:
Total surface area = Triangle face area + Parallelogram face area + Rectangle face area
Total surface area = 24 + 60 + 190 = 274 square inches
Given that one pint of paint covers 200 square inches, we need to determine how many pints of paint the skateboard club needs to purchase:
Number of pints = Total surface area / Area covered by one pint
Number of pints = 274 / 200 ≈ 1.37
Since paint is only sold in whole pints, the skateboard club would need to purchase 2 pints of paint to cover the entire ramp model.
Given:
- Height (h) = 6 inches
- Long side of the triangle (b) = 10 inches
- Base of the triangle (given it's half the base of the parallelogram) = 8 inches
- Width (w) = 19 inches
First, we will calculate the area of the triangle face:
Area of a triangle = 0.5 * base * height
Area of the triangle face = 0.5 * 8 * 6 = 24 square inches
Next, we will calculate the area of the parallelogram face:
Area of a parallelogram = base * height
Area of the parallelogram face = 10 * 6 = 60 square inches
Now, calculate the area of the rectangle face:
Area of a rectangle = length * width
Area of the rectangle face = 10 * 19 = 190 square inches
Total surface area to be painted:
Total surface area = Triangle face area + Parallelogram face area + Rectangle face area
Total surface area = 24 + 60 + 190 = 274 square inches
Given that one pint of paint covers 200 square inches, we need to determine how many pints of paint the skateboard club needs to purchase:
Number of pints = Total surface area / Area covered by one pint
Number of pints = 274 / 200 ≈ 1.37
Since paint is only sold in whole pints, the skateboard club would need to purchase 2 pints of paint to cover the entire ramp model.
1 answer