1. What is the slant height for the given pyramid to the nearest whole unit?
Pyramid base = 10 cm
Height = 12 cm
A. 7 cm
B. 11 cm
C. 13 cm
D. 16 cm
2. What is the length of the diagonal for the given rectangular prism to the nearest whole unit?
Legnth= 8cm
Width= 3cm
Height= 7cm
A. 10 cm
B. 11 cm
C. 6 cm
D. 13 cm
Please help!!
1. s^2 = (10/2)^2 + 12^2
2. d^2 = L^2 + W^2 + H^2
So what's the exact answer?
Thank you, scott!
1. 13
2. 11
Sure! Let's break down each question and explain how to find the answers step-by-step:
1. To find the slant height of a pyramid, you can use the Pythagorean Theorem. The slant height is the hypotenuse of a right triangle formed by the height of the pyramid and half the length of the base.
In this case, the height of the pyramid is given as 12 cm, and the base length is given as 10 cm. We need to find half the length of the base, which is 10 cm divided by 2, resulting in 5 cm.
Now we have a right triangle with two sides, one being the height of 12 cm and the other being half the length of the base, which is 5 cm. We can use the Pythagorean Theorem:
Hypotenuse^2 = Height^2 + Base/2^2
Plugging in the values, we get:
Hypotenuse^2 = 12^2 + 5^2
Hypotenuse^2 = 144 + 25
Hypotenuse^2 = 169
To find the slant height, we need to take the square root of both sides to cancel out the square on the right side:
Hypotenuse = √169
Hypotenuse = 13
Since we are asked for the answer to the nearest whole unit, the slant height is 13 cm.
Therefore, the answer is:
C. 13 cm
2. To find the length of the diagonal of a rectangular prism, you can also use the Pythagorean Theorem. The diagonal of a rectangular prism is the hypotenuse of a right triangle formed by the length, width, and height of the prism.
In this case, the length is given as 8 cm, width as 3 cm, and height as 7 cm.
We can use the Pythagorean Theorem to find the diagonal:
Diagonal^2 = Length^2 + Width^2 + Height^2
Plugging in the values, we get:
Diagonal^2 = 8^2 + 3^2 + 7^2
Diagonal^2 = 64 + 9 + 49
Diagonal^2 = 122
To find the length of the diagonal, we need to take the square root of both sides:
Diagonal = √122
Approximating the square root to the nearest whole unit:
Diagonal ≈ √122 ≈ 11
Therefore, the answer is:
B. 11 cm
I hope this helps! Let me know if you have any other questions.
17. A cone has a radius of 24cm and a volume of 1920cm2. what is the volume of a similar come with a radius of 18cm?
A. 480cm3
B. 810cm3***
C. 1080cm3
D. 1440cm3
is my answer correct?