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 physics units and measurement: error analysis significant figures significant figures and rounding of digits units and measurements

The volume of a sphere is $ 1.76\;{cm }^{ 3 }$. The volume of 25 such spheres according to the idea of significant figures in ${cm}^{ 3 }$ is 

  1. 44.00

  2. 44.0

  3. 44

  4. 4.4
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Volume of 1 sphere $=1.76 cm^{3}$
Volume of 25 spheres $=25\times 1.76$
                                      $=44 {cm}^{3}$
                                      $=44.0 {cm}^{3}$
                                 (Since volume is reported in 3 significant figure)

Multiple choice physics units and measurement: error analysis significant figures significant figures and rounding of digits units and measurements

The radius of sphere is measured to be $\displaystyle \left ( 2.1\pm 0.5 \right )$cm.
 Calculate its surface area with error limits.

  1. $\displaystyle S=\left ( 55.4\pm 26.4 \right )cm^{2}$
  2. $\displaystyle S=\left ( 55.4\pm 26.4 \right )mm^{2}$
  3. $\displaystyle S=\left ( 55.4\pm 13.2 \right )cm^{2}$

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

Surface area, $\displaystyle S=4\pi r^{2}=\left ( 4 \right )\left ( \frac{22}{7} \right )\left ( 2.1 \right )^{2}$$\displaystyle =55.44=55.4cm^{2}$
Further, $\displaystyle \frac{\Delta S}{S}=2.\frac{\Delta r}{r}$
              $\displaystyle \Delta S=2\left ( \frac{\Delta r}{r} \right )\left ( S \right )=\frac{2\times 0.5\times 55.4}{2.1}$$\displaystyle =26.38=26.4 cm^{2}$

$\displaystyle \therefore S=\left ( 55.4\pm 26.4 \right )cm^{2}$

Multiple choice

What is the formula for the volume of a sphere?

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

The formula for the volume of a sphere is (V = \frac{4}{3} \pi r^3), where (r) is the radius of the sphere.

Multiple choice

The ancient Indian mathematical text, the 'Ganita Sara Samgraha', contains a formula for calculating the volume of a sphere. What is the formula?

  1. Volume = (4/3) * π * radius^3

  2. Volume = π * radius^2

  3. Volume = (1/3) * π * radius^3

  4. Volume = (2/3) * π * radius^3
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The Ganita Sara Samgraha provides a formula for calculating the volume of a sphere, which is Volume = (4/3) * π * radius^3.

Multiple choice

What is the volume of a sphere with radius 5?

  1. 125\pi

  2. 250\pi

  3. 375\pi

  4. 500\pi
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The volume of a sphere with radius r is given by the formula (V = \frac{4}{3}\pi r^3). Substituting r = 5 into the formula, we get: (V = \frac{4}{3}\pi (5^3) = \frac{4}{3}\pi \cdot 125 = 375\pi). Therefore, the volume of the sphere is 375\pi.

Multiple choice

What is the name of the theorem that states that the volume of a sphere is equal to two-thirds the product of its surface area and radius?

  1. Pythagorean Theorem

  2. Triangle Inequality Theorem

  3. Angle Sum Theorem

  4. Volume of a Sphere Formula
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The Volume of a Sphere Formula states that the volume of a sphere is equal to two-thirds the product of its surface area and radius. This formula is attributed to Indian mathematicians.

Multiple choice

The surface area of a sphere is given by the formula:

  1. A = 4πr^2

  2. A = πr^2

  3. A = 2πr^2
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The surface area of a sphere is given by the formula A = 4πr^2, where r is the radius of the sphere.

Multiple choice

A sphere is a three-dimensional geometric figure that is defined by a fixed point (the center) and a fixed distance (the radius) from the center to any point on the sphere. What is the volume of a sphere with radius 3?

  1. 36π

  2. 72π

  3. 108π

  4. 144π
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 (4/3)πr^3. Therefore, the volume of a sphere with radius 3 is (4/3)π * 3^3 = 36π.

Multiple choice

A sphere is a three-dimensional geometric figure that is defined by a fixed point (the center) and a fixed distance (the radius) from the center to any point on the sphere. What is the surface area of a sphere with radius 5?

  1. 100π

  2. 200π

  3. 300π

  4. 400π
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The surface area of a sphere with radius r is given by the formula 4πr^2. Therefore, the surface area of a sphere with radius 5 is 4π * 5^2 = 100π.

Multiple choice

What is the volume of a sphere with radius 6?

  1. 36π

  2. 72π

  3. 108π

  4. 144π
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The volume of a sphere is given by the formula $V = (4/3)πr^3$. Substituting the given value, we get $V = (4/3)π(6)^3 = 36π$.

Multiple choice

What is the name of the theorem that states that the volume of a sphere is equal to four-thirds pi times the cube of its radius?

  1. Pythagorean theorem

  2. Brahmagupta theorem

  3. Angle sum theorem

  4. Volume of a sphere formula
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The volume of a sphere formula states that the volume of a sphere is equal to four-thirds pi times the cube of its radius.

Multiple choice

What is the name of the theorem that states that the surface area of a sphere is equal to four pi times the square of its radius?

  1. Pythagorean theorem

  2. Brahmagupta theorem

  3. Angle sum theorem

  4. Surface area of a sphere formula
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The surface area of a sphere formula states that the surface area of a sphere is equal to four pi times the square of its radius.

Multiple choice

What is the name of the theorem that states that the volume of a sphere is equal to four-thirds pi times the cube of its radius?

  1. Pythagorean theorem

  2. Brahmagupta theorem

  3. Angle sum theorem

  4. Volume of a sphere formula
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The volume of a sphere formula states that the volume of a sphere is equal to four-thirds pi times the cube of its radius.

Multiple choice

What is the name of the theorem that states that the surface area of a sphere is equal to four pi times the square of its radius?

  1. Pythagorean theorem

  2. Brahmagupta theorem

  3. Angle sum theorem

  4. Surface area of a sphere formula
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The surface area of a sphere formula states that the surface area of a sphere is equal to four pi times the square of its radius.

Multiple choice

What is the name of the theorem that states that the volume of a sphere is equal to 4/3 pi times the cube of its radius?

  1. Pythagorean Theorem

  2. Brahmagupta's Theorem

  3. Euclid's Theorem

  4. Volume of a Sphere Formula
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The Volume of a Sphere Formula is a well-known formula for finding the volume of a sphere.