1. Find the length of the height of the cone
d = 10 cm wide
13 cm high
2. Given L = 30 in, W = 20 in, h = 18 in, and x = 36.1 in. Find the length of D. Round the answer to the nearest tenth.
3. For the square pyramid, the lateral edge length, e, is 25 in., and the slant height, s, is 24 in. Find the height of the pyramid, h. Round the answer to the nearest whole number. Hint: Before finding the length of h, you will first need to find the length of r.
4. The Pyramid is an arena in Memphis, Tennessee. Its height is 321 ft., and its slant height is 436.5 ft. Find the length of the edge of the square base. Round the answer to the nearest tenth.
5. A juice can is in the shape of a cylinder. It has a height of 122 mm and a diameter of 52 mm. What is the longest straw that can fit completely inside the juice can diagonally? Round the answer to the nearest tenth.
1. 12
2. 40.3
3. 23
4. 591.6
5. 132.6
1. The length of the height of the cone can be found using the Pythagorean theorem.
The diameter of the cone is 10 cm, which means the radius is half of that, so r = 5 cm.
The height of the cone is given as 13 cm.
Using the Pythagorean theorem, we have:
r^2 + h^2 = d^2
5^2 + h^2 = 10^2
25 + h^2 = 100
h^2 = 75
h = √75
h ≈ 8.7 cm
Therefore, the length of the height of the cone is approximately 8.7 cm.
2. To find the length of D, we can use the Pythagorean theorem.
We are given L = 30 in, W = 20 in, h = 18 in, and x = 36.1 in.
Using the Pythagorean theorem, we have:
L^2 + W^2 = D^2
30^2 + 20^2 = D^2
900 + 400 = D^2
1300 = D^2
D = √1300
D ≈ 36.1 in
Therefore, the length of D is approximately 36.1 in.
3. To find the height of the pyramid, we first need to find the length of r using the given slant height and lateral edge length.
We are given lateral edge length e = 25 in and slant height s = 24 in.
Using the Pythagorean theorem, we have:
r^2 = s^2 - (e/2)^2
r^2 = 24^2 - (25/2)^2
r^2 = 576 - 6.25
r^2 = 569.75
r ≈ √569.75
r ≈ 23.9 in
Now that we have the length of r, we can find the height h using the Pythagorean theorem:
h^2 = s^2 - r^2
h^2 = 24^2 - 23.9^2
h^2 = 576 - 570.21
h^2 ≈ 5.79
h ≈ √5.79
h ≈ 2.4 in (rounded to the nearest whole number)
Therefore, the height of the pyramid is approximately 2 inches.
4. To find the length of the edge of the square base, we can use the Pythagorean theorem.
We are given the height h = 321 ft and slant height s = 436.5 ft.
Using the Pythagorean theorem, we have:
s^2 = h^2 + (edge length)^2
436.5^2 = 321^2 + (edge length)^2
190096.25 = 103041 + (edge length)^2
87055.25 = (edge length)^2
edge length ≈ √87055.25
edge length ≈ 295.1 ft (rounded to the nearest tenth)
Therefore, the length of the edge of the square base is approximately 295.1 ft.
5. To find the longest straw that can fit completely inside the juice can diagonally, we can use the Pythagorean theorem.
The height of the juice can is 122 mm and the diameter is 52 mm, which means the radius is half of that, so r = 26 mm.
Using the Pythagorean theorem, we have:
d^2 = h^2 + r^2
d^2 = 122^2 + 26^2
d^2 = 14884 + 676
d^2 = 15560
d ≈ √15560
d ≈ 124.6 mm (rounded to the nearest tenth)
Therefore, the longest straw that can fit completely inside the juice can diagonally is approximately 124.6 mm.