A cone has a radious of 24 cm and a volume of 1,920 cm ^3. what is the volume of a similar cone with a radius of 18 cm?
What Is the surface area of a sphere with a radius of 4 meters rounded to the nearest square meter?
What is the volume of a sphere with a radius of 6 meters rounded to the nearest square meter?
What is the length of the diagonal fro the given rectangular prism to the nearest whole unit?
Length: 6 cm
Width: 5 cm
Height: 9 cm
Please help me! I'm super confused
The volume of similar figures is proportional to the cube of the corresponding sides,
so V/1920 = 18^3/24^3 = 3^3/4^3 = 27/64
64V = 27*1920
V = 27*1920/64 = 810
The volume is 810 cm^3
2. You must know the formula for the surface area of a cube, then sub in the values.
Tell me what you got
3. You must know the formula for the volume of a cube, then sub in the values.
Tell me what you got
4. L^2 = √(6^2 + 5^2 + 9^2)
= ....
L = √....
In #2 and #3, I meant sphere , not cube
what’s the volume of the square with the height of 5, 5 width, and 5 length?
Sure, I can help you with these questions!
Question 1: To find the volume of a similar cone, we can use the concept of similar shapes. The ratio of the radii of the two cones is 24/18 = 4/3. Since volume is proportional to the cube of the radius, we can set up the following equation:
(24/18)^3 = (1,920/V2)
Solving for V2 (the volume of the smaller cone):
V2 = (1,920)(3/4)^3 = (1,920)(27/64) = 810 cm^3
So, the volume of the similar cone with a radius of 18 cm is 810 cm^3.
Question 2: The formula for the surface area of a sphere is given by A = 4πr^2, where r is the radius. To find the surface area of a sphere with a radius of 4 meters:
A = 4π(4^2) = 4π(16) = 64π square meters
Since you want the answer rounded to the nearest square meter, we can use the value of π as approximately 3.14 and round the result:
A ≈ 64(3.14) ≈ 201 square meters
Therefore, the surface area of the sphere is approximately 201 square meters.
Question 3: The formula for the volume of a sphere is given by V = (4/3)πr^3, where r is the radius. To find the volume of a sphere with a radius of 6 meters:
V = (4/3)π(6^3) = (4/3)π(216) = 288π cubic meters
Using the value of π as approximately 3.14, we can round the result to the nearest square meter:
V ≈ 288(3.14) ≈ 905 cubic meters
Therefore, the volume of the sphere is approximately 905 cubic meters.
Question 4: To find the length of the diagonal of a rectangular prism, we can use the Pythagorean theorem. The diagonal (D) is the hypotenuse of a right triangle formed by the length (L), width (W), and height (H) of the prism. The Pythagorean theorem states that:
D^2 = L^2 + W^2 + H^2
Substituting the given values:
D^2 = 6^2 + 5^2 + 9^2 = 36 + 25 + 81 = 142
To find the length of the diagonal (D), we take the square root of 142:
D ≈ √142 ≈ 11.92
Rounding to the nearest whole unit, the length of the diagonal is approximately 12 units.
I hope this helps clarify the solutions to your questions! Let me know if you have any further inquiries.