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 general knowledge math & puzzles

When a metallic ball bearing is placed inside a cylindrical container, of radius 2 cm, the height of the water, inside the container, increases by 0.6 cm. The radius, to the nearest tenth of a centimeter, of the ball bearing is

  1. 1

  2. 1.2

  3. 2

  4. 0.6
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The volume of water displaced is V = π * r^2 * h = π * 2^2 * 0.6 = 2.4π. The volume of the ball (sphere) is (4/3)π * R^3. Setting 2.4π = (4/3)π * R^3 gives R^3 = 1.8. The cube root of 1.8 is approximately 1.216, which rounds to 1.2.

Multiple choice general knowledge culture

Ball must be spherical, made of leather or synthetic leather, have a circumference of 65–67 cm, a lighter weight of 260–280 g and an inside air pressure of 0.30–0.325 kg/cm2. Use clue if u cannot get it still.

  1. Volleyball Ball

  2. Rugby Ball

  3. Water Polo Ball

  4. Basketball Ball
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A volleyball matches these specs: 65-67cm circumference, 260-280g (lighter than football/basketball), and low air pressure of 0.30-0.325 kg/cm2. The weight and pressure are key distinguishing features.

Multiple choice general knowledge science & technology

When a metallic ball bearing is placed inside a cylindrical container, of radius 2 cm, the height of the water, inside the container, increases by 0.6 cm. The radius, to the nearest tenth of a centimeter, of the ball bearing is

  1. 1 cm

  2. 1.2 cm

  3. 2 cm

  4. 0.6 cm
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The ball displaces water equal to its volume. Ball volume = (4/3)πr³. Displaced water volume = π(2)²(0.6) = 2.4π. Equating: (4/3)πr³ = 2.4π, which gives r³ = 1.8 and r ≈ 1.2 cm.

Multiple choice general knowledge math & puzzles

Which of the following has has the largest surface area to volume ratio?

  1. Tetrahedron

  2. Cube

  3. Sphere

  4. Dodecahedron
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For similar volumes, simpler shapes with fewer faces have higher surface-area-to-volume ratios. A tetrahedron (4 faces) has the highest ratio among these options because it's the most 'pointy' shape with maximum surface exposure. A sphere has the lowest SA:V ratio for a given volume, which is why cells and organisms approximate spherical shapes to minimize surface area.

Multiple choice technology programming languages

Trying determine the shape of a cylindrical can made from 1000 cm2 of tin that has the largest possible volume is an example of:

  1. Array calculation

  2. Text manipulation

  3. Optimization problem

  4. Object oriented programming
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

This is a classic optimization problem - finding the dimensions of a cylinder that maximize volume given a fixed surface area constraint. Such problems use calculus (derivatives to find maxima/minima) to determine optimal solutions.

Multiple choice

A cylinder is 6 cms in diameter and 6 cms in height. If spheres of the same size are made from the material obtained, what is the diameter of each sphere?

  1. 5 cms

  2. 2 cms

  3. 3 cms

  4. 4 cms

Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The cylinder volume is π × r² × h = π × 3² × 6 = 54π cubic cm. If spheres of diameter 3cm (radius 1.5cm) are made, each sphere has volume (4/3)π × 1.5³ = 4.5π. The number of spheres is 54π / 4.5π = 12, which is valid. Alternatively, if the question means the cylinder is recast into spheres of the same diameter as the cylinder's height, then diameter = 3cm.

Multiple choice

The size of a colloidal particle is

  1. About 10-10 m

  2. 10 -9 -10 -7 m

  3. Greater than 10 -7 m

  4. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Colloidal particles are intermediate in size between true solutions and suspensions, typically ranging from 1 nanometer to 100 nanometers (10^-9 to 10^-7 m).