To find the largest size sphere that can fit in a cube box, we need to identify the diameter of the sphere.
In a cube, the space diagonal (d) can be found by using the formula:
d = s√3,
where s is the length of any side of the cube.
Given that the side length of the cube is 20 cm, we can calculate the space diagonal:
d = 20√3.
The diameter of the sphere will be equal to the space diagonal, which is 20√3 cm.
Now, to calculate the surface area of the sphere (A), we use the formula:
A = 4πr²,
where r is the radius of the sphere.
Since the diameter (d) is equal to 20√3 cm, the radius (r) will be half of the diameter, so:
r = (20√3)/2,
r = 10√3 cm.
Plugging this value into the surface area formula, we get:
A = 4π(10√3)²,
A = 4π(300),
A = 1200π.
Therefore, the surface area of the largest size sphere that can fit in the cube box is 1200π square cm.
Hey Bot I need a bit of help?
A cube box is 20 cm×20 cm× 20 cm . What is the surface area of the largest size sphere that can fit in this box? Leave your answer in terms of pi.(1 point)
9 answers
That didn't work for me.Can you try again, I'm trying to understand what they want me to do for this one?
Apologies for any confusion. Let's approach the problem differently.
To find the surface area of the largest sphere that can fit in the cube box, we need to determine the radius of the sphere.
In a cube, the diagonal (d) connecting opposite corners passes through the center. This diagonal length is equal to the diameter of the sphere that can fit inside the cube.
Using the Pythagorean theorem, we can find the length of the diagonal (d):
d = √(20^2 + 20^2 + 20^2),
d = √(400 + 400 + 400),
d = √1200,
d = 20√3.
Therefore, the diameter of the sphere is 20√3 cm, and the radius (r) of the sphere is half of this value:
r = (20√3)/2,
r = 10√3 cm.
Now, to find the surface area of the sphere (A), we can use the formula:
A = 4πr^2.
Plugging in the value of the radius, we get:
A = 4π(10√3)^2,
A = 4π(100 × 3),
A = 4π(300),
A = 1200π.
Hence, the surface area of the largest size sphere that can fit in the cube box is 1200π square cm.
To find the surface area of the largest sphere that can fit in the cube box, we need to determine the radius of the sphere.
In a cube, the diagonal (d) connecting opposite corners passes through the center. This diagonal length is equal to the diameter of the sphere that can fit inside the cube.
Using the Pythagorean theorem, we can find the length of the diagonal (d):
d = √(20^2 + 20^2 + 20^2),
d = √(400 + 400 + 400),
d = √1200,
d = 20√3.
Therefore, the diameter of the sphere is 20√3 cm, and the radius (r) of the sphere is half of this value:
r = (20√3)/2,
r = 10√3 cm.
Now, to find the surface area of the sphere (A), we can use the formula:
A = 4πr^2.
Plugging in the value of the radius, we get:
A = 4π(10√3)^2,
A = 4π(100 × 3),
A = 4π(300),
A = 1200π.
Hence, the surface area of the largest size sphere that can fit in the cube box is 1200π square cm.
I'm saying Bot that, that isn't the answer
Apologies for the confusion. Let's try again.
To find the largest size sphere that can fit in a cube, the sphere should have a diameter equal to the length of a side of the cube.
In this case, the cube has sides measuring 20 cm each. Therefore, the diameter of the sphere should also be 20 cm.
The surface area (A) of a sphere can be calculated using the formula:
A = 4πr^2,
where r is the radius of the sphere.
Since the diameter is 20 cm, the radius (r) will be half of that:
r = 20/2 = 10 cm.
Now, we can substitute the value of the radius into the surface area formula:
A = 4π(10)^2,
A = 4π(100),
A = 400π.
Hence, the surface area of the largest size sphere that can fit in the cube box is 400π square cm.
To find the largest size sphere that can fit in a cube, the sphere should have a diameter equal to the length of a side of the cube.
In this case, the cube has sides measuring 20 cm each. Therefore, the diameter of the sphere should also be 20 cm.
The surface area (A) of a sphere can be calculated using the formula:
A = 4πr^2,
where r is the radius of the sphere.
Since the diameter is 20 cm, the radius (r) will be half of that:
r = 20/2 = 10 cm.
Now, we can substitute the value of the radius into the surface area formula:
A = 4π(10)^2,
A = 4π(100),
A = 400π.
Hence, the surface area of the largest size sphere that can fit in the cube box is 400π square cm.
Thanks Bot, That worked now I understand a bit better but what am I supposed to do with this one ?
A rectangular box is 12 in. × 14 in. × 18 in. What is the surface area of the largest size sphere that could fit in this box? Leave your answer in terms of pi.(1 point)
A rectangular box is 12 in. × 14 in. × 18 in. What is the surface area of the largest size sphere that could fit in this box? Leave your answer in terms of pi.(1 point)
To determine the surface area of the largest sphere that can fit in the rectangular box, we need to find the diameter of the sphere.
The sphere should have a diameter equal to the shortest dimension of the box to ensure it fits inside.
In this case, the shortest dimension is 12 inches. Therefore, the diameter of the sphere should also be 12 inches.
The surface area (A) of a sphere can be calculated using the formula:
A = 4πr²,
where r is the radius of the sphere.
Since the diameter is 12 inches, the radius (r) will be half of that:
r = 12/2 = 6 inches.
Now we can calculate the surface area of the sphere:
A = 4π(6)²,
A = 4π(36),
A = 144π.
Hence, the surface area of the largest size sphere that can fit in the rectangular box is 144π square inches.
The sphere should have a diameter equal to the shortest dimension of the box to ensure it fits inside.
In this case, the shortest dimension is 12 inches. Therefore, the diameter of the sphere should also be 12 inches.
The surface area (A) of a sphere can be calculated using the formula:
A = 4πr²,
where r is the radius of the sphere.
Since the diameter is 12 inches, the radius (r) will be half of that:
r = 12/2 = 6 inches.
Now we can calculate the surface area of the sphere:
A = 4π(6)²,
A = 4π(36),
A = 144π.
Hence, the surface area of the largest size sphere that can fit in the rectangular box is 144π square inches.
Thank you Bot that also worked, and now I know what to do!
You're welcome! I'm glad I could help, and I'm glad to hear that you now understand what to do. If you have any more questions, feel free to ask.