What is the two-dimensional shape created by the sliced object?
A. Rectangle
B. Triangle
C. Hexagon
D. Parallelogram
11 answers
B. Triangle
What is a two-dimensional representation of a three-dimensional figure?
A. A square
B. A rectangle
C. A cube
D. A net
A. A square
B. A rectangle
C. A cube
D. A net
D. A net
Could you explain how its D. A net?
Certainly! A net is a two-dimensional representation of a three-dimensional figure that can be folded to form the actual three-dimensional shape. It shows all the faces of the three-dimensional figure laid out flat, allowing you to see how the shape is constructed. For example, a net of a cube would show all six squares that make up the cube when folded and assembled. It's like an unfolded cube map.
What is the missing length of a rectangular prism where the height and width are both 9 cm and the surface area is 432 cm^2?
To find the missing length of the rectangular prism, we need to use the formula for the surface area of a rectangular prism, which is given by:
Surface Area = 2lw + 2lh + 2wh
Given:
Height (h) = 9 cm
Width (w) = 9 cm
Surface Area = 432 cm^2
Plugging in the values:
432 = 2(9)(w) + 2(9)(9) + 2(w)(9)
432 = 18w + 162 + 18w
432 = 36w + 162
432 - 162 = 36w
270 = 36w
w = 7.5
Therefore, the missing length of the rectangular prism is 7.5 cm.
Surface Area = 2lw + 2lh + 2wh
Given:
Height (h) = 9 cm
Width (w) = 9 cm
Surface Area = 432 cm^2
Plugging in the values:
432 = 2(9)(w) + 2(9)(9) + 2(w)(9)
432 = 18w + 162 + 18w
432 = 36w + 162
432 - 162 = 36w
270 = 36w
w = 7.5
Therefore, the missing length of the rectangular prism is 7.5 cm.
13 cm = up and down
7.5 = side to side
Calculate the surface area of the cylinder. Give both exact and approximate answers. Round the approximate answer to the nearest hundredth. Use pi= 3.14
Exact answer: ____pi cm^2
Approximate answer: ____ cm^2
7.5 = side to side
Calculate the surface area of the cylinder. Give both exact and approximate answers. Round the approximate answer to the nearest hundredth. Use pi= 3.14
Exact answer: ____pi cm^2
Approximate answer: ____ cm^2
Given:
Radius (r) = 7.5 cm
Height (h) = 13 cm
π = 3.14
Exact surface area of a cylinder formula: 2πr(r + h)
Exact calculation: 2 * 3.14 * 7.5(7.5 + 13)
Exact calculation: 2 * 3.14 * 7.5 * 20.5
Exact calculation: 3.14 * 150
Exact answer: 471π cm^2
Approximate calculation: 471π ≈ 471 * 3.14
Approximate calculation: 1479.94 cm^2
Therefore, the surface area of the cylinder is approximately 1479.94 cm^2.
Radius (r) = 7.5 cm
Height (h) = 13 cm
π = 3.14
Exact surface area of a cylinder formula: 2πr(r + h)
Exact calculation: 2 * 3.14 * 7.5(7.5 + 13)
Exact calculation: 2 * 3.14 * 7.5 * 20.5
Exact calculation: 3.14 * 150
Exact answer: 471π cm^2
Approximate calculation: 471π ≈ 471 * 3.14
Approximate calculation: 1479.94 cm^2
Therefore, the surface area of the cylinder is approximately 1479.94 cm^2.
Which cylinder has a different surface area than the others?
A. 5 cm = side to side
55 cm = up and down
B. 12 cm = side to side
14 cm = up and down
C. 10 cm = side to side
20 cm = up and down
D. 15 cm = side to side
5 cm = up and down
A. 5 cm = side to side
55 cm = up and down
B. 12 cm = side to side
14 cm = up and down
C. 10 cm = side to side
20 cm = up and down
D. 15 cm = side to side
5 cm = up and down
To calculate the surface area of each cylinder, you can use the formula for the surface area of a cylinder, which is given by:
Surface Area = 2πr(r+h)
Let's calculate the surface area of each cylinder:
A:
Radius (r) = 5 cm
Height (h) = 55 cm
Surface Area = 2π(5)(5+55) = 2π(5)(60) = 600π cm^2
B:
Radius (r) = 12 cm
Height (h) = 14 cm
Surface Area = 2π(12)(12+14) = 2π(12)(26) = 624π cm^2
C:
Radius (r) = 10 cm
Height (h) = 20 cm
Surface Area = 2π(10)(10+20) = 2π(10)(30) = 600π cm^2
D:
Radius (r) = 15 cm
Height (h) = 5 cm
Surface Area = 2π(15)(15+5) = 2π(15)(20) = 600π cm^2
Comparing the surface areas, we see that cylinders A, C, and D all have a surface area of 600π cm^2, while cylinder B has a surface area of 624π cm^2. Therefore, cylinder B has a different surface area than the others.
Surface Area = 2πr(r+h)
Let's calculate the surface area of each cylinder:
A:
Radius (r) = 5 cm
Height (h) = 55 cm
Surface Area = 2π(5)(5+55) = 2π(5)(60) = 600π cm^2
B:
Radius (r) = 12 cm
Height (h) = 14 cm
Surface Area = 2π(12)(12+14) = 2π(12)(26) = 624π cm^2
C:
Radius (r) = 10 cm
Height (h) = 20 cm
Surface Area = 2π(10)(10+20) = 2π(10)(30) = 600π cm^2
D:
Radius (r) = 15 cm
Height (h) = 5 cm
Surface Area = 2π(15)(15+5) = 2π(15)(20) = 600π cm^2
Comparing the surface areas, we see that cylinders A, C, and D all have a surface area of 600π cm^2, while cylinder B has a surface area of 624π cm^2. Therefore, cylinder B has a different surface area than the others.