Question
a ball will fit inside a cubed box and will touch all 6 sides. the surface area of the ball is 1017.36 square inches. what is the length of each side of the box. use 3.14 for pi. PLEASE HAVE THE RIGHT ANSWER I DONT HAVE TIME FOR A LYING AND INCORRECT BOT
Answers
Answer
How much larger, in volume, is one large ball that has a radius of 21 inches than the total volume of 3 balls that each have a radius of 4 inches? Use 3.14 for pi. PLEASE HAVE THE RIGHT ANSWER I DONT HAVE TIME FOR A LYING AND INCORRECT BOT
Answer
find the height and volume of a cone with slant height of 41 feet and a radius of 40 feet. PLEASE HAVE THE RIGHT ANSWER I DONT HAVE TIME FOR A LYING AND INCORRECT BOT
Answered by
GPT 3.5
The surface area of a sphere is given by the formula 4πr^2, where r is the radius of the sphere. Since the surface area of the ball is 1017.36 square inches, we can set up the equation:
4πr^2 = 1017.36
Solving for the radius:
r^2 = 1017.36 / 4π
r^2 ≈ 81.0
r ≈ 9
The diameter of the sphere, which is equal to the length of each side of the cube, is equal to 2r:
2r ≈ 2(9) = 18
Therefore, the length of each side of the box is 18 inches.
4πr^2 = 1017.36
Solving for the radius:
r^2 = 1017.36 / 4π
r^2 ≈ 81.0
r ≈ 9
The diameter of the sphere, which is equal to the length of each side of the cube, is equal to 2r:
2r ≈ 2(9) = 18
Therefore, the length of each side of the box is 18 inches.
Answered by
GPT 3.5
To calculate the volume of a sphere, you can use the formula V = (4/3)πr^3, where r is the radius of the sphere.
For the large ball with a radius of 21 inches:
V_large = (4/3)(3.14)(21^3)
V_large ≈ 38949.52 in^3
For each small ball with a radius of 4 inches:
V_small = (4/3)(3.14)(4^3)
V_small ≈ 268.19 in^3
The total volume of 3 small balls:
V_total_small = 3 * V_small
V_total_small ≈ 804.57 in^3
The difference in volume:
Difference = V_large - V_total_small
Difference ≈ 38144.95 in^3
Therefore, the large ball with a radius of 21 inches is approximately 38144.95 cubic inches larger in volume than the total volume of 3 balls with a radius of 4 inches.
For the large ball with a radius of 21 inches:
V_large = (4/3)(3.14)(21^3)
V_large ≈ 38949.52 in^3
For each small ball with a radius of 4 inches:
V_small = (4/3)(3.14)(4^3)
V_small ≈ 268.19 in^3
The total volume of 3 small balls:
V_total_small = 3 * V_small
V_total_small ≈ 804.57 in^3
The difference in volume:
Difference = V_large - V_total_small
Difference ≈ 38144.95 in^3
Therefore, the large ball with a radius of 21 inches is approximately 38144.95 cubic inches larger in volume than the total volume of 3 balls with a radius of 4 inches.
Answered by
GPT 3.5
To find the height and volume of a cone, you can use the formulas:
1. Slant height (l) of the cone: l = √(r^2 + h^2)
2. Volume (V) of the cone: V = (1/3)πr^2h
Given:
Slant height (l) = 41 ft
Radius (r) = 40 ft
1. Find the height (h) using the slant height (l) and the radius (r):
l = √(r^2 + h^2)
41 = √(40^2 + h^2)
41 = √(1600 + h^2)
41^2 = 1600 + h^2
1681 = 1600 + h^2
h^2 = 1681 - 1600
h^2 = 81
h = √81
h = 9 ft
2. Calculate the volume (V) of the cone using the height (h) and radius (r):
V = (1/3)πr^2h
V = (1/3)(3.14)(40^2)(9)
V = (1/3)(3.14)(1600)(9)
V = (1/3)(3.14)(14400)
V = 15072 ft^3
Therefore, the height of the cone is 9 feet and the volume of the cone is 15072 cubic feet.
1. Slant height (l) of the cone: l = √(r^2 + h^2)
2. Volume (V) of the cone: V = (1/3)πr^2h
Given:
Slant height (l) = 41 ft
Radius (r) = 40 ft
1. Find the height (h) using the slant height (l) and the radius (r):
l = √(r^2 + h^2)
41 = √(40^2 + h^2)
41 = √(1600 + h^2)
41^2 = 1600 + h^2
1681 = 1600 + h^2
h^2 = 1681 - 1600
h^2 = 81
h = √81
h = 9 ft
2. Calculate the volume (V) of the cone using the height (h) and radius (r):
V = (1/3)πr^2h
V = (1/3)(3.14)(40^2)(9)
V = (1/3)(3.14)(1600)(9)
V = (1/3)(3.14)(14400)
V = 15072 ft^3
Therefore, the height of the cone is 9 feet and the volume of the cone is 15072 cubic feet.