apply the pythagorean theorem to determine the height of the square pyramid, h. round the answer to the nearest tenth
A.32.0
B.15.0
C.47.2
D.31.2
To find the length of the diagonal of the rectangular prism, we can use the Pythagorean theorem. Let's call the length of the diagonal of the rectangular prism "d".
We are given the length (32 cm), width (24 cm), and height (44 cm) of the rectangular prism, and the length of the diagonal of the base segment BH (40 cm).
Using the Pythagorean theorem, we have:
d^2 = 32^2 + 24^2 + 44^2
d^2 = 1024 + 576 + 1936
d^2 = 3536
Taking the square root of both sides, we find:
d ≈ 59.5
Therefore, the length of the diagonal of the rectangular prism, rounded to the nearest tenth, is 59.5.
Answer: D. 59.5
To find the slant height of the paper cone, we can use the Pythagorean theorem. Let's call the slant height "s", the radius "r", and the height "h".
Given that the height of the cone is 6 cm and the diameter is 13 cm, we can calculate the radius:
r = diameter / 2 = 13 cm / 2 = 6.5 cm
Now, we can use the Pythagorean theorem:
s^2 = r^2 + h^2
s^2 = (6.5 cm)^2 + (6 cm)^2
s^2 = 42.25 cm^2 + 36 cm^2
s^2 = 78.25 cm^2
Taking the square root of both sides, we find:
s ≈ 8.8 cm
Therefore, the slant height of the paper cone, rounded to the nearest tenth, is 8.8 cm.
Answer: 8.8
To find the slant height of the paper cone, we can use the Pythagorean theorem. Let's call the slant height "s", the radius "r", and the height "h".
Given that the height of the cone is 6 cm and the diameter is 13 cm, we can calculate the radius:
r = diameter / 2 = 13 cm / 2 = 6.5 cm
Now, we can use the Pythagorean theorem:
s^2 = r^2 + h^2
s^2 = (6.5 cm)^2 + (6 cm)^2
s^2 = 42.25 cm^2 + 36 cm^2
s^2 = 78.25 cm^2
Taking the square root of both sides, we find:
s ≈ 8.8 cm
Therefore, the slant height of the paper cone, rounded to the nearest tenth, is 8.8 cm.
Answer: C. 8.8
To find the height of the tent, we can use the Pythagorean theorem. Let's call the height of the tent "h" and the slant height "s".
Given that the slant height is 13.5 m, we can use the Pythagorean theorem:
h^2 = s^2 - a^2
Where "a" is half the length of the base square (since each edge is 20 m).
So, a = 20 m / 2 = 10 m
h^2 = (13.5 m)^2 - (10 m)^2
h^2 = 182.25 m^2 - 100 m^2
h^2 = 82.25 m^2
Taking the square root of both sides, we find:
h ≈ 9.1 m
Therefore, the height of the tent, rounded to the nearest tenth, is 9.1 m.
Answer: B. 9.1
Unfortunately, the information provided is insufficient to apply the Pythagorean theorem and determine the height of the square pyramid. 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. To apply the theorem, we need to know the lengths of the other sides of the triangle.
those lengths that you need are 25 and 40, please answer with with the answers ive provided you with
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
A.54.4
B.46.2
C.51.6
D.59.5
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.
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
A.14.3
B.11.5
C.8.8
D.2.5
The circus tent is in the shape of a square pyramid each edge of the square base is 20 m and it’s slant height is 13.5 m find the height of the tent round the answer to the nearest tenth
A.14.8
B.9.1
C.24.1
D.16.8
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 a 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 around your answer to the nearest tenth.
A.60.2
B.92.9
C.78.6
D.116.3
Using the Pythagorean theorem, we can determine the height of the square pyramid. Let's call the height of the pyramid "h".
The Pythagorean theorem states that
a^2 + b^2 = c^2
where "a" and "b" are the lengths of the two sides forming the right angle, and "c" is the length of the hypotenuse. In this case, the sides "a" and "b" are 25 and 40, respectively.
25^2 + 40^2 = h^2
625 + 1600 = h^2
2225 = h^2
Taking the square root of both sides, we find:
h ≈ 47.2
Therefore, the height of the square pyramid, rounded to the nearest tenth, is 47.2.
Answer: C. 47.2
To find the length of the ramp needed to fit diagonally in the cage, we can use the Pythagorean theorem. Let's call the length of the ramp "r", the length of the cage "l", the width of the cage "w", and the height of the cage "h".
Given that the length of the cage is 70 cm, the width is 35 cm, and the height is 50 cm, we can calculate the diagonal length of the base of the cage using the Pythagorean theorem:
d^2 = l^2 + w^2
d^2 = (70 cm)^2 + (35 cm)^2
d^2 = 4900 cm^2 + 1225 cm^2
d^2 = 6125 cm^2
Taking the square root of both sides, we find:
d ≈ 78.3 cm
Now, we need to find the length of the ramp, which would be the height of the cage. Given that the height is 50 cm, we have:
r^2 = d^2 + h^2
(78.3 cm)^2 = (50 cm)^2 + h^2
6108.09 cm^2 = 2500 cm^2 + h^2
h^2 = 6108.09 cm^2 - 2500 cm^2
h^2 = 3608.09 cm^2
Taking the square root of both sides, we find:
h ≈ 60.1 cm
Therefore, the length of the ramp needed to fit diagonally in the cage, rounded to the nearest tenth, is 60.1 cm.
Answer: A. 60.2 cm