Table of Contents
- 1 What is the volume of a sphere inscribed in a cube?
- 2 What is the area of the surface of a sphere inscribed in a cube?
- 3 What will happen to the volume of a cylinder if its radius is doubled and height is halved?
- 4 What is the maximum possible volume of a cube that can fit inside?
- 5 How do you find the volume of an inscribed sphere?
- 6 What is the volume of circumscribing sphere in square root?
What is the volume of a sphere inscribed in a cube?
If s is the side length of the cube, we have that Vcube=s3. Notice that the largest possible sphere that can fit inside the cube is the inscribed sphere, which has radius 12s. Using the volume formula for a sphere, we find that Vsphere=43πr3=43πs38=π6s3.
Is inscribed in a cube then the ratio of the volume of cube to the volume of sphere will be?
If a sphere is inscribed in a cube, then the ratio of the volume of the cube to the volume of the sphere will be 6 : π.
What is the area of the surface of a sphere inscribed in a cube?
Correct answer: The side of the cube is the same as the diameter of the sphere. Since d = 4, r = 2. The surface area of a sphere is found by SA = 4π(r2) = 4π(22) = 16π.
What is the maximum possible volume of a cube in cubic inches that could be inscribed inside a sphere with a radius of 3 inches?
a√3=2 ==>a=2/√3(diagonal of cube=diameter of sphere). Hence volume of cube=a^3=8/3√3. The longest rod that can be kept inside a cube is root 3 * a, where a is edge of the cube. This length is the diameter of the sphere, which is given as 2 units.
What will happen to the volume of a cylinder if its radius is doubled and height is halved?
If the radius of a cylinder is doubled and height is halved, the volume will be doubled.
What is the maximum possible volume of a sphere that can fit inside a cube of side 6 cm?
So, for the largest sphere in a cube, the diameter of the sphere will be equal to side of the cube. Therefore, the volume of the largest sphere inside the given cube is 36 π .
What is the maximum possible volume of a cube that can fit inside?
a√3=2 ==>a=2/√3(diagonal of cube=diameter of sphere). Hence volume of cube=a^3=8/3√3. So answer will be root of 3 * (8/9) = 1.54 (approx) .
What is the volume of a large cube?
The volume of a cube is determined by multiplying the length of three edges of the cube. Let “a” define the length of an edge of the cube. This formula is also written as V = a³.
How do you find the volume of an inscribed sphere?
Given a cube with a side length S the volume (V) of an inscribed sphere can be found by substituting the formula for finding the R adius of an inscribed sphere into the formula for finding the V olume of a sphere.
What is the volume of a sphere in Pi units?
The volume of sphere = (2/3) πr 2 (2r) It becomes, V = 4/3 πr 3. Therefore, The volume of a sphere= 4/3 πr 3 Cubic units. You can easily find the volume of the sphere and equation of sphere if you have the measurements of the radius.
What is the volume of circumscribing sphere in square root?
The diameter D of the sphere is equal to the space diagonal s of the cube. Thus, From the above results, it is clear that the volume of circumscribing sphere is square root of 27 times larger than the volume of inscribed sphere.
What is the volume of a sphere whose radius is R?
To calculate the sphere volume, whose radius is ‘r’ we have the below formula: Volume of a sphere = 4/3 πr3 Now let us learn here to derive this formula and also solve some questions with us to master the concept. If you consider a circle and a sphere, both are round.