can anyone help me with these 2 questions pls?
Calculate the slant height for the given cone. Round to the nearest tenth.
(1 point)
Diameter = 8
Height = 9
10.2 cm
11.4 cm
9.8 cm
12.0 cm
Calculate the length of the diagonal for the given rectangular prism. Round to the nearest tenth.
(1 point)
Length = 14
Width = 3
Height = 4
16.7
14.3
14.8***
15.6
i don't know the first one:( and i am not 100% sure on the 2nd one...
can someone pls help me asap!??
thanx in advance
I assume you mean the diameter of the circular base of the cone, so the radius is 4
slant-height^2 = 9^2 + 4^2 = 97
slant-height = √97 = appr 9.85
your second question is correct
Sure, I'll be happy to help you with these questions!
For the first question, to calculate the slant height of a cone, you can use the Pythagorean Theorem. The slant height is the hypotenuse of a right triangle formed by the height and the radius (half the diameter) of the cone.
In this case, the diameter of the cone is given as 8, so the radius is 8/2 = 4. The height is given as 9. Using the Pythagorean theorem, we can calculate the slant height as follows:
slant height^2 = radius^2 + height^2
slant height^2 = 4^2 + 9^2
slant height^2 = 16 + 81
slant height^2 = 97
To find the slant height, we take the square root of both sides:
slant height = √97
Now we can round this value to the nearest tenth. Looking at the answer choices, we can see that the value closest to √97 rounded to the nearest tenth is 9.8 cm.
So, the answer to the first question is 9.8 cm.
For the second question, to calculate the length of the diagonal of a rectangular prism, we can use the Pythagorean Theorem as well. The diagonal is the hypotenuse of a right triangle formed by the length, width, and height of the rectangular prism.
In this case, the length is given as 14, the width as 3, and the height as 4. Using the Pythagorean theorem, we can calculate the diagonal as follows:
diagonal^2 = length^2 + width^2 + height^2
diagonal^2 = 14^2 + 3^2 + 4^2
diagonal^2 = 196 + 9 + 16
diagonal^2 = 221
To find the diagonal, we take the square root of both sides:
diagonal = √221
Now we can round this value to the nearest tenth. Looking at the answer choices, we can see that 14.8 is the value closest to √221 rounded to the nearest tenth.
So, the answer to the second question is 14.8.
I hope this helps! If you have any further questions, feel free to ask.