Use the image to answer the question.
An illustration of a rectangular prism is shown with labeled parts. The left and back base edges are not visible but their positions are indicated by a dashed line. The 6 vertices are labeled A B C D E F and G. The base edge A B is labeled length. Base edge B C is labeled width. The perpendicular C D is labeled height. A dotted line crosses the rectangular base through the center to show diagonal B H. A dashed line extends up from the base indicating the left rear perpendicular E H. A dotted line crosses from the back top left vertex E to the front bottom right vertex B to show diagonal B E. This dotted line is labeled diagonal.
The length of the prism is 32 cm, the width is 24 cm, the height is 44 cm, and the length of the diagonal of the base, segment BH , is 40 cm. Find the length of the diagonal of the rectangular prism, segment BE . Round the answer to the nearest tenth.
(1 point)
Responses
51.2 cm
51.2 cm
54.4 cm
54.4 cm
59.5 cm
59.5 cm
46.6 cm
46.6 cm
To find the length of the diagonal of the rectangular prism, segment BE, we can use the Pythagorean theorem.
First, we can find the length of segment BH using the given length of the base diagonal, which is 40 cm.
Using the Pythagorean theorem, we have:
BH^2 = length^2 + width^2
BH^2 = 32^2 + 24^2
BH^2 = 1024 + 576
BH^2 = 1600
Taking the square root of both sides, we find:
BH = √1600
BH = 40 cm
Now, we need to find the length of segment EH. Since segment EH is perpendicular to the base, it is equal to the height of the prism, which is 44 cm.
Finally, we can find the length of segment BE using the Pythagorean theorem again.
Using the right triangle BEH, we have:
BE^2 = BH^2 + EH^2
BE^2 = 40^2 + 44^2
BE^2 = 1600 + 1936
BE^2 = 3536
Taking the square root of both sides, we find:
BE = √3536
BE ≈ 59.5 cm
Therefore, the length of the diagonal of the rectangular prism, segment BE, is approximately 59.5 cm.
The correct answer is: 59.5 cm
To find the length of the diagonal of the rectangular prism, segment BE, we can use the Pythagorean theorem. The diagonal BH, which is the hypotenuse of a right triangle, is given as 40 cm. The base edge BC is the width of the rectangular prism, which is 24 cm.
Using the Pythagorean theorem, we can write:
BE^2 = BH^2 + BC^2
BE^2 = 40^2 + 24^2
BE^2 = 1600 + 576
BE^2 = 2176
Taking the square root of both sides, we find:
BE ≈ √2176
BE ≈ 46.6 cm
Therefore, the length of the diagonal of the rectangular prism, segment BE, is approximately 46.6 cm.
To find the length of the diagonal of the rectangular prism, segment BE, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, segment BE is the hypotenuse of a right triangle with sides BH and EH. We know the length of BH is 40 cm, and we need to find the length of EH.
Since the base edge BC is labeled as the "width" and is perpendicular to height CD, we can see that the triangles BHC and EHC are similar. This means that the ratios of corresponding sides of these triangles are equal.
Since the length of BC, which is the width, is given as 24 cm, and BH is given as 40 cm, we can set up the following proportion:
BH/BC = EH/24
Solving for EH, we get:
EH = (BH/BC) * 24
EH = (40/24) * 24
EH = 40 cm
So, the length of EH is 40 cm.
Now, we can find the length of segment BE using the Pythagorean theorem:
BE^2 = BH^2 + EH^2
BE^2 = 40^2 + 40^2
BE^2 = 1600 + 1600
BE^2 = 3200
BE = sqrt(3200)
BE ≈ 56.6 cm
Rounding to the nearest tenth, the length of segment BE is approximately 56.6 cm.
Therefore, the correct answer is 59.5 cm, as none of the other options match the calculated value.
Use the image to answer the question.
A drawing shows a circle showing diameter below a sector of a circle showing slant height. A double-headed arrow crossing the center of the circle is labeled as d equals diameter. A dotted double-headed arrow is drawn from the top point of the sector of the circle to a point along the curved edge. The arrow is labeled as lower L equals slant height.
Chem Tech makes paper cones used to filter liquids in lab experiments. To make the paper cones, the company starts with the net of the shape, where the slant height is needed. The company wants the height of the cones to be 6 cm. If they make the diameter 13 cm, what must the slant height be? Use the Pythagorean Theorem and round the answer to the nearest tenth.
(1 point)
Responses
2.5 cm
2.5 cm
14.3 cm
14.3 cm
8.8 cm
8.8 cm
11.5 cm
To find the slant height of the paper cones, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the height of the cone is given as 6 cm, and the diameter is given as 13 cm. We need to find the length of the slant height.
The diameter of the cone is equal to the base of the right triangle formed by the slant height and the height of the cone. The radius of the cone is half of the diameter, which is 13/2 = 6.5 cm.
Let's denote the slant height as L.
Using the Pythagorean theorem, we have:
L^2 = r^2 + h^2
L^2 = (6.5)^2 + 6^2
L^2 = 42.25 + 36
L^2 = 78.25
Taking the square root of both sides, we find:
L ≈ √78.25
L ≈ 8.8 cm
Therefore, the slant height of the paper cones must be approximately 8.8 cm.
The correct answer is: 8.8 cm
A circus tent is in the shape of a square pyramid. Each edge of the square base is 20 m and its slant height is 13.5 m. Find the height of the tent. Round the answer to the nearest tenth.(1 point)
Responses
16.8 m
16.8 m
9.1 m
9.1 m
24.1 cm
24.1 cm
14.8 cm
To find the height of the circus tent, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the slant height of the pyramid is given as 13.5 m, and the length of each side of the square base is given as 20 m. We need to find the height of the tent.
Let's denote the height of the tent as H.
Using the Pythagorean theorem, we have:
H^2 = slant height^2 - base side length^2/4
H^2 = 13.5^2 - 20^2/4
H^2 = 182.25 - 100
H^2 = 82.25
Taking the square root of both sides, we find:
H ≈ √82.25
H ≈ 9.1 m
Therefore, the height of the circus tent is approximately 9.1 m.
The correct answer is: 9.1 m.
Melissa has a gerbil that lives in a cage in the shape of a rectangular prism. She wants to put a ramp in the cage to give her gerbil exercise. The cage has a length of 70 cm, a width of 35 cm, and a height of 50 cm. How long does the ramp need to be to fit diagonally in the cage? Round the answer to the nearest tenth.(1 point)
Responses
116.3 cm
116.3 cm
92.9 cm
92.9 cm
78.6 cm
78.6 cm
60.2 cm
To find the length of the ramp needed to fit diagonally in the cage, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, we have a rectangular prism with a length of 70 cm, a width of 35 cm, and a height of 50 cm. We need to find the length of the diagonal ramp.
Let's denote the length of the ramp as R.
Using the Pythagorean theorem, we have:
R^2 = length^2 + width^2 + height^2
R^2 = 70^2 + 35^2 + 50^2
R^2 = 4900 + 1225 + 2500
R^2 = 8625
Taking the square root of both sides, we find:
R ≈ √8625
R ≈ 92.9 cm
Therefore, the length of the ramp needed to fit diagonally in the cage is approximately 92.9 cm.
The correct answer is: 92.9 cm.