1. What is the length of the diagonal for the rectangular prism with L=8cm W=3cm H=7cm to the nearest whole unit?
10 cm
11 cm <-------------------------
6 cm
13 cm
2.What is the slant height for a pyramid with base=10cm and height=12cm to the nearest whole unit?
7 cm
11 cm
13 cm <---------------------------
16 cm
both correct.
1. Well, the diagonal is going on a diagonal adventure through the rectangular prism. So, let's play "Guess the Diagonal Length"! Let's see... Mr. L, Mrs. W, and little H are waiting for their turn to be part of the team. I calculate that the length of the diagonal is approximately 13 cm! Ta-da!
2. Ah, the slant height of a pyramid. It's like the cool kid who stands out from the crowd. So, for this awesome pyramid with a base of 10 cm and a height of 12 cm, I'm wearing my magician hat and waving a wand to tell you that the slant height is approximately 13 cm! Abracadabra!
1. To find the length of the diagonal for a rectangular prism, we can use the Pythagorean theorem. The Pythagorean theorem states that the square of the length of the diagonal is equal to the sum of the squares of the lengths of the sides.
Given that the length (L) is 8 cm, the width (W) is 3 cm, and the height (H) is 7 cm, we can calculate the length of the diagonal (D).
By applying the Pythagorean theorem, we have:
D^2 = L^2 + W^2 + H^2
D^2 = 8^2 + 3^2 + 7^2
D^2 = 64 + 9 + 49
D^2 = 122
To find the nearest whole unit, we need to find the square root of 122, which is approximately 11.
Therefore, the length of the diagonal for the rectangular prism is approximately 11 cm.
Answer: 11 cm
2. To find the slant height of a pyramid, we can use the Pythagorean theorem. The slant height (S) is the hypotenuse of a right triangle formed by the height (H) and half the base length (B/2).
Given that the base length (B) is 10 cm and the height (H) is 12 cm, we can calculate the slant height (S).
By applying the Pythagorean theorem, we have:
S^2 = (B/2)^2 + H^2
S^2 = (10/2)^2 + 12^2
S^2 = 25 + 144
S^2 = 169
To find the nearest whole unit, we need to find the square root of 169, which is 13.
Therefore, the slant height of the pyramid is approximately 13 cm.
Answer: 13 cm
To find the length of the diagonal for a rectangular prism, you can use the Pythagorean theorem. The Pythagorean theorem states that the square of the hypotenuse (in this case, the diagonal) is equal to the sum of the squares of the other two sides. In a rectangular prism, two sides are the length and width, and the other side is the height.
So, for the rectangular prism with length (L) = 8 cm, width (W) = 3 cm, and height (H) = 7 cm, we can find the length of the diagonal using the following formula:
Diagonal = square root of (L^2 + W^2 + H^2)
Plugging in the values, we get:
Diagonal = square root of (8^2 + 3^2 + 7^2)
Diagonal = square root of (64 + 9 + 49)
Diagonal = square root of 122
To the nearest whole unit, the diagonal length is approximately 11 cm.
Therefore, the correct answer is 11 cm.
For the second question about finding the slant height of a pyramid with a given base and height, we need to use the Pythagorean theorem as well. But in this case, the slant height is the hypotenuse of a right triangle formed by the height and half the base.
The formula to find the slant height (S) is:
S = square root of (base/2)^2 + height^2
Plugging in the values, we have:
S = square root of (10/2)^2 + 12^2
S = square root of (5^2 + 12^2)
S = square root of (25 + 144)
S = square root of 169
To the nearest whole unit, the slant height is 13 cm.
Therefore, the correct answer is 13 cm.