Mathematics · Physics

Sphere Geometry

183 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 is an air-filled sphere with a circumference of 68–70 cm (27–28 in), a heavier weight 410–450 g (14–16 oz), inflated to a pressure of 0.6–1.1 at (59–108 kPa 8.5–15.6 psi) "at sea level", and covered in leather. Use clue if u cannot get it still.

  1. Football Ball

  2. Volleyball Ball

  3. Rugby Ball

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

A football (soccer ball) fits this description perfectly: 68-70cm circumference, 410-450g weight, leather-covered, inflated to specific pressure. The dimensions and weight match FIFA specifications exactly.

Multiple choice general knowledge culture

Official diameter is 65.41-68.58 mm (2.575-2.700 inches). Balls must weigh between 56.0g and 59.4g (1.975-2.095 ounces). Balls are covered in a fibrous fluffy felt which modifies their aerodynamic properties. Made of rubber with a cloth covering. Use clue if u cannot get it still.

  1. Lawn Tennis Ball

  2. Squash Ball

  3. Polo Ball

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

A tennis ball is distinguished by: 65.41-68.58mm diameter, 56-59.4g weight, rubber core, and the characteristic fibrous felt covering. The fuzzy felt is unique to tennis balls among sports balls.

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 culture

Ball is 720–730 mm (28–29 in) in circumference, and 545–555 mm (21.5–21.9 in) transverse circumference, and inflated to a pressure of 62–76 kPa (9.0–11.0 psi). Shaped like an egg. Use clue if u cannot get it still.

  1. Volleyball Ball

  2. Football Ball

  3. Rugby Ball

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

A rugby ball is characterized by its egg/oval shape, 720-730mm long circumference, 545-555mm transverse circumference, and inflated to 62-76 kPa. The egg shape is the key identifier.

Multiple choice general knowledge culture

Balls are 39.5 mm and 40.5 mm in diameter, and have a mass of 23 to 25 grams.[4] They are made with two pieces of rubber compound, glued together to form a hollow sphere and buffed to a matte finish. Different balls are provided for varying temperature and atmospheric conditions and standards of play. Use clue if u cannot get it still.

  1. Polo Ball

  2. Lawn Tennis Ball

  3. Squash Ball

  4. Golf ball
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A squash ball matches: 39.5-40.5mm diameter, 23-25g mass, made of two pieces of rubber compound glued into a hollow sphere, with matte finish. The small rubber construction is characteristic.

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.