To apply the Pythagorean Theorem to determine the height of the square pyramid, we can use the right triangle formed by the height line, the slant height, and the dotted line from the center of the base to the center of the right base edge.
Let's label the slant height as c, the height line as a, and the dotted line from the center of the base to the center of the right base edge as b.
According to the Pythagorean Theorem, the sum of the squares of the two shorter sides of a right triangle is equal to the square of the hypotenuse. In this case, we have:
a^2 + b^2 = c^2
Squaring the slant height of 25 feet, we have:
25^2 = a^2 + 40^2
625 = a^2 + 1600
a^2 = 625 - 1600
a^2 = -975
Since we cannot have a negative value for the height, we can conclude that the height of the square pyramid, h, is not a real number. Therefore, none of the given response options (47.2 ft, 32.0 ft, 15.0 ft, 31.2 ft) are correct.
Use the image to answer the question.
An illustration shows a square pyramid with labeled parts. The left, front and right faces of the pyramid and base are visible. The back face is not visible. The back base edge is not visible but its position is indicated by a dashed line. The front base edge shows a length of 40 feet. A dotted line extends from the interior of the vertex straight down to the center of the base and is labeled h. A right angle is indicated where the dotted height line meets the base. Another dotted line extends from the center of the base where the height line meets to the center of the right base edge. A dotted line extends from the right base edge straight up the center of the right face of the prism and meets the height line at the vertex. This dotted line shows a slant height of 25 feet.
Apply the Pythagorean Theorem to determine the height of the square pyramid, h. Round the answer to the nearest tenth.
(1 point)
Responses
47.2 ft.
47.2 ft.
32.0 ft.
32.0 ft.
15.0 ft.
15.0 ft.
31.2 ft.
9 answers
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
54.4 cm
54.4 cm
51.2 cm
51.2 cm
59.5 cm
59.5 cm
46.6 cm
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
54.4 cm
54.4 cm
51.2 cm
51.2 cm
59.5 cm
59.5 cm
46.6 cm
To find the length of the diagonal of the rectangular prism, segment BE, we can use the Pythagorean Theorem.
Let's label the length of the prism as a, the width as b, the height as c, the length of the diagonal of the base (segment BH) as d, and the length of the diagonal of the rectangular prism (segment BE) as x.
According to the Pythagorean Theorem, for a right-angled triangle, the sum of the squares of the two shorter sides is equal to the square of the hypotenuse. In this case, we have:
x^2 = a^2 + b^2 + c^2
Plugging in the given values, we have:
x^2 = 32^2 + 24^2 + 44^2
x^2 = 1024 + 576 + 1936
x^2 = 3536
Taking the square root of both sides, we have:
x ≈ √3536
x ≈ 59.5 cm
Thus, the length of the diagonal of the rectangular prism, segment BE, is approximately 59.5 cm. Therefore, the correct response is 59.5 cm.
Let's label the length of the prism as a, the width as b, the height as c, the length of the diagonal of the base (segment BH) as d, and the length of the diagonal of the rectangular prism (segment BE) as x.
According to the Pythagorean Theorem, for a right-angled triangle, the sum of the squares of the two shorter sides is equal to the square of the hypotenuse. In this case, we have:
x^2 = a^2 + b^2 + c^2
Plugging in the given values, we have:
x^2 = 32^2 + 24^2 + 44^2
x^2 = 1024 + 576 + 1936
x^2 = 3536
Taking the square root of both sides, we have:
x ≈ √3536
x ≈ 59.5 cm
Thus, the length of the diagonal of the rectangular prism, segment BE, is approximately 59.5 cm. Therefore, the correct response is 59.5 cm.
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
11.5 cm
11.5 cm
8.8 cm
8.8 cm
2.5 cm
2.5 cm
14.3 cm
14.3 cm
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
11.5 cm
11.5 cm
8.8 cm
8.8 cm
2.5 cm
2.5 cm
14.3 cm
14.3 cm
To find the slant height of the cone, we can use the Pythagorean Theorem.
Let's label the diameter of the cone as d, the slant height as L, and the height as h.
According to the Pythagorean Theorem, in a right-angled triangle, the sum of the squares of the two shorter sides is equal to the square of the hypotenuse. In this case, we have:
L^2 = (d/2)^2 + h^2
Plugging in the given values, we have:
L^2 = (13/2)^2 + 6^2
L^2 = (6.5)^2 + 6^2
L^2 = 42.25 + 36
L^2 = 78.25
Taking the square root of both sides, we have:
L ≈ √78.25
L ≈ 8.8 cm
Thus, the slant height of the cone must be approximately 8.8 cm. Therefore, the correct response is 8.8 cm.
Let's label the diameter of the cone as d, the slant height as L, and the height as h.
According to the Pythagorean Theorem, in a right-angled triangle, the sum of the squares of the two shorter sides is equal to the square of the hypotenuse. In this case, we have:
L^2 = (d/2)^2 + h^2
Plugging in the given values, we have:
L^2 = (13/2)^2 + 6^2
L^2 = (6.5)^2 + 6^2
L^2 = 42.25 + 36
L^2 = 78.25
Taking the square root of both sides, we have:
L ≈ √78.25
L ≈ 8.8 cm
Thus, the slant height of the cone must be approximately 8.8 cm. Therefore, the correct response 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
24.1 cm
24.1 cm
14.8 cm
14.8 cm
9.1 m
9.1 m
16.8 m
Responses
24.1 cm
24.1 cm
14.8 cm
14.8 cm
9.1 m
9.1 m
16.8 m
To find the height of the square pyramid tent, we can use the Pythagorean Theorem.
Let's label the height of the tent as h, the slant height as s, and the half of the length of the square base as a.
According to the Pythagorean Theorem, in a right-angled triangle, the sum of the squares of the two shorter sides is equal to the square of the hypotenuse. In this case, we have:
h^2 = s^2 - a^2
Plugging in the given values, we have:
h^2 = 13.5^2 - 10^2
h^2 = 182.25 - 100
h^2 = 82.25
Taking the square root of both sides, we have:
h ≈ √82.25
h ≈ 9.1 m
Thus, the height of the circus tent is approximately 9.1 m. Therefore, the correct response is 9.1 m.
Let's label the height of the tent as h, the slant height as s, and the half of the length of the square base as a.
According to the Pythagorean Theorem, in a right-angled triangle, the sum of the squares of the two shorter sides is equal to the square of the hypotenuse. In this case, we have:
h^2 = s^2 - a^2
Plugging in the given values, we have:
h^2 = 13.5^2 - 10^2
h^2 = 182.25 - 100
h^2 = 82.25
Taking the square root of both sides, we have:
h ≈ √82.25
h ≈ 9.1 m
Thus, the height of the circus tent is approximately 9.1 m. Therefore, the correct response 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
78.6 cm
78.6 cm
92.9 cm
92.9 cm
60.2 cm
60.2 cm
116.3 cm
Responses
78.6 cm
78.6 cm
92.9 cm
92.9 cm
60.2 cm
60.2 cm
116.3 cm
To find the length of the ramp needed to fit diagonally in the cage, we can use the Pythagorean Theorem.
Let's label the length of the cage as L, the width as W, the height as H, and the length of the ramp as R.
According to the Pythagorean Theorem, in a right-angled triangle, the sum of the squares of the two shorter sides is equal to the square of the hypotenuse. In this case, we have:
R^2 = L^2 + W^2 + H^2
Plugging in the given values, we have:
R^2 = 70^2 + 35^2 + 50^2
R^2 = 4900 + 1225 + 2500
R^2 = 8625
Taking the square root of both sides, we have:
R ≈ √8625
R ≈ 92.9 cm
Thus, the length of the ramp needed to fit diagonally in the cage is approximately 92.9 cm. Therefore, the correct response is 92.9 cm.
Let's label the length of the cage as L, the width as W, the height as H, and the length of the ramp as R.
According to the Pythagorean Theorem, in a right-angled triangle, the sum of the squares of the two shorter sides is equal to the square of the hypotenuse. In this case, we have:
R^2 = L^2 + W^2 + H^2
Plugging in the given values, we have:
R^2 = 70^2 + 35^2 + 50^2
R^2 = 4900 + 1225 + 2500
R^2 = 8625
Taking the square root of both sides, we have:
R ≈ √8625
R ≈ 92.9 cm
Thus, the length of the ramp needed to fit diagonally in the cage is approximately 92.9 cm. Therefore, the correct response is 92.9 cm.