Mathematics · Physics

Sphere Geometry

157 Questions

Sphere geometry deals with calculating the volume and surface area of round objects. It includes problems on spherical shells, recasting spheres, and understanding radius variations. These mathematical formulas are essential for competitive exam preparation.

Volume of a sphereSurface area calculationsSpherical shellsRadius ratio variationsRecasting spheres

Sphere Geometry Questions

Multiple choice

What is the volume of a sphere with radius (r)?

  1. \(\frac{4}{3}\pi r^3\)
  2. \(\frac{1}{3}\pi r^3\)
  3. \(\pi r^3\)
  4. \(2\pi r^3\)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The volume of a sphere is given by (\frac{4}{3}\pi r^3), where (r) is the radius of the sphere.

Multiple choice

What is the surface area of a sphere with radius (r)?

  1. \(4\pi r^2\)
  2. \(2\pi r^2\)
  3. \(\pi r^2\)
  4. \(\frac{1}{2}\pi r^2\)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The surface area of a sphere is given by (4\pi r^2), where (r) is the radius of the sphere.

Multiple choice

A sphere has a radius of (5) centimeters. What is the volume of the sphere?

  1. \(523.6\) cm³
  2. \(339.2\) cm³
  3. \(267.9\) cm³
  4. \(133.9\) cm³
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The volume of a sphere is given by (\frac{4}{3}\pi r^3). Substituting (r = 5) cm, we get (\frac{4}{3}\pi (5)^3 = 523.6) cm³.

Multiple choice

A sphere has a surface area of (144) square centimeters. What is the radius of the sphere?

  1. \(3\) cm
  2. \(4\) cm
  3. \(5\) cm
  4. \(6\) cm
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The surface area of a sphere is given by (4\pi r^2). Solving for (r), we get (r = \sqrt{\frac{A}{4\pi}}). Substituting (A = 144) cm², we get (r = \sqrt{\frac{144}{4\pi}} = 4) cm.

Multiple choice

What is the center of mass of a hollow sphere?

  1. The center of the sphere

  2. The surface of the sphere

  3. The midpoint of a diameter of the sphere

  4. The edge of the sphere
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The center of mass of a hollow sphere is the center of the sphere. This is because the mass of the sphere is evenly distributed throughout its volume, even though there is no mass at the center of the sphere.

Multiple choice

What is the formula for calculating the total surface area of a sphere?

  1. TSA = 4 * π * r^2

  2. TSA = 2 * π * r * h

  3. TSA = π * r

  4. TSA = 2 * π * r^2 * h
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The formula for calculating the total surface area of a sphere is TSA = 4 * π * r^2, where r is the radius of the sphere.

Multiple choice

In the 2011 China Girls' Mathematical Olympiad, what was the volume of a sphere with radius 7 cm?

  1. 143π cm^3

  2. 286π cm^3

  3. 429π cm^3

  4. 572π cm^3
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The volume of a sphere with radius r is given by the formula V = (4/3)πr^3. Plugging in the value r = 7, we get V = (4/3)π(7)^3 = 143π cm^3.