Jeni is painting a flattened shoebox for a school project. The shoebox measures 72.5 cm x 47.5 cm x 104 cm. What is one area that would be identified on the box’s net?(1 point)
Responses
31,847.5 cm2
7,540 cm2
358,150 cm2
224 cm2
One area that would be identified on the box's net is the base, which has an area of 72.5 cm x 47.5 cm = 3443.75 cm².
no
I apologize for the incorrect response earlier. To identify one area on the shoebox's net, we need to consider the individual faces of the box. The net of a shoebox consists of six faces, which, when unfolded and laid flat, make up the complete box.
One face of the box could be the top or lid of the shoebox, which has an area of 72.5 cm x 47.5 cm = 3443.75 cm². Another face could be the bottom of the box, which also has the same area of 3443.75 cm².
Another face could be the front or back of the box, which has an area of 104cm x 47.5cm = 4940 cm². The other face opposite to it would have the same area.
Finally, the remaining two faces correspond to the sides of the box, which each have an area of 104 cm x 72.5 cm = 7540 cm².
Therefore, depending on which face of the shoebox's net we are looking at, we could identify an area of 3443.75 cm², 4940 cm², or 7540 cm².
ok
I hope that helps! Let me know if you have any further questions.
What is the surface area of a rectangular prism whose dimensions are 3 3/4 dm × 4 1/2 dm × 5 dm in square decimeters?(1 point)
To find the surface area of a rectangular prism, we need to find the area of all six faces of the prism and then add them up.
The dimensions of the rectangular prism are given as 3 3/4 dm × 4 1/2 dm × 5 dm. We can convert these dimensions to decimeters by multiplying them by 0.1.
So, we have:
- Length = 3 3/4 dm = 3.75 dm
- Width = 4 1/2 dm = 4.5 dm
- Height = 5 dm
Now, we can find the area of each face of the rectangular prism:
- Front and back faces: Length × Height = 3.75 dm × 5 dm = 18.75 dm² (two faces, so total area is 2 × 18.75 dm² = 37.5 dm²)
- Top and bottom faces: Width × Height = 4.5 dm × 5 dm = 22.5 dm² (two faces, so total area is 2 × 22.5 dm² = 45 dm²)
- Side faces: Length × Width = 3.75 dm × 4.5 dm = 16.875 dm² (two faces, so total area is 2 × 16.875 dm² = 33.75 dm²)
Now, we can add up the areas of all six faces to get the total surface area:
37.5 dm² + 45 dm² + 33.75 dm² = 116.25 dm²
Therefore, the surface area of the rectangular prism is 116.25 square decimeters.
Apply the technique of using nets to find the surface area of a turtle’s tank, which measures 33.93 inches long by 15.81 inches wide by 17.69 inches tall. What is the surface area of the tank if the tank does not include a top cover? Round the answer to the nearest hundredth.(1 point)
Responses
2,832.67 in2
2,832.67 in squared
9,489.51 in2
9,489.51 in squared
2,296.23 in2
2,296.23 in squared
1,416.33 in2
To find the surface area of a turtle's tank, we can use the technique of using nets. A net is a 2-dimensional shape that, when folded and glued or taped, forms a 3-dimensional object. In this case, we can create a net by drawing the top and bottom faces of the tank and two side faces with tabs that fold up to form the front and back faces and another two side faces with tabs that fold up to form the two ends of the tank.
Once we have created the net, we can measure the dimensions of each face and calculate the area of each face. Finally, we can add up all the areas to find the total surface area of the tank.
Here's a breakdown of the calculations:
- Top and bottom faces: Length × Width = 33.93 in × 15.81 in = 537.03 in² (two faces, so total area is 2 × 537.03 in² = 1,074.06 in²)
- Front and back faces: Height × Width = 17.69 in × 15.81 in = 279.49 in² (two faces, so total area is 2 × 279.49 in² = 558.98 in²)
- Side faces: Length × Height = 33.93 in × 17.69 in = 600.20 in² (two faces, so total area is 2 × 600.20 in² = 1,200.40 in²)
Now, we can add up the areas of all six faces to get the total surface area:
1,074.06 in² + 558.98 in² + 1,200.40 in² = 2,833.44 in²
Rounding to the nearest hundredth, the surface area of the turtle's tank is 2,832.67 in².
Therefore, the closest answer choice is 2,832.67 in².