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 nearestent.
If anyone is wondering what are all of the answers here they are also im 8th grade so yeah
answers
15.0 for number 1
59.5 for number 2
8.8 for number 3
9.1 for number 4
92.9 for number 5
and that's for the Pythagorean Theorem in Three Dimensions quick check and if you want ill give you the practice here are the answers for that
number 1 is 12
number 2 is 40.3
number 3 is 23
number 4 is 591.6
and number 5 is 132.6
hope this helps
59.5
46.6
51.2
54.4
To find the slant height of the cone, we need to use the formula for the slant height of a right circular cone, which is given by the Pythagorean theorem:
slant height^2 = height^2 + radius^2.
Given that the height is 6 cm and the diameter is 13 cm (which means the radius is half of the diameter, so the radius is 6.5 cm), we can substitute these values into the formula:
slant height^2 = 6^2 + 6.5^2
slant height^2 = 36 + 42.25
slant height^2 = 78.25.
To find the slant height, we need to take the square root of both sides:
slant height = √78.25
slant height ≈ 8.84 cm.
Therefore, the slant height of the cone should be approximately 8.84 cm.
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.
the options are
59.5
46.6
51.2
54.4
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)
To find the height of the tent, we can use the Pythagorean theorem.
The slant height is given as 13.5 m, and the length of each edge of the square base is 20 m. Let's label the height of the pyramid as "h".
Using the Pythagorean theorem, we have:
h^2 = slant height^2 - (1/2 * square base length)^2
h^2 = 13.5^2 - (1/2 * 20)^2
h^2 = 182.25 - 100
h^2 = 82.25
To find the height, we need to take the square root of both sides:
h = √82.25
h ≈ 9.1 m
Therefore, the height of the tent is approximately 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 amp need to be to fit diagonally in the cage? Round the answer to the nearest tenth. (1 point)
To find the length of the ramp needed to fit diagonally in the cage, we can use the Pythagorean theorem.
The length, width, and height of the cage form a right triangle, where the diagonal of the cage will act as the hypotenuse of this triangle. Let's denote the length of the ramp needed 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
To find the length of the ramp, we need to take the square root of both sides:
r ≈ √8625
r ≈ 92.9 cm
Therefore, the length of the ramp needed to fit diagonally in the cage is approximately 92.9 cm.