Explanation

The surface area of a sphere depends only on the radius (r) and is given by the formula 4πr².

This formula comes from calculus and represents the total area covering the outer layer of a perfect sphere.

Explanation

(n - 2)180° formula calculates the sum of all internal angles of an n-sided polygon.

It works because any polygon can be divided into (n - 2) triangles.

Explanation

The number of elements in B × A is found by multiplying the number of elements in B and A:

|B| × |A| = 4 × 2 = 8

Each ordered pair has one element from B and one from A.

Explanation

The alternendo property states that if a/b = c/d, then:

a/c = b/d

Explanation

Area of a square = side × side = 8 × 8 = 64 m²

Explanation

To convert degrees to radians:

  Radians = Degrees × (π / 180)

  45 × (π / 180) = π/4

Explanation

48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

64: 1, 2, 4, 8, 16, 32, 64

120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120

The highest common factor (HCF) among these numbers is: 8

Explanation

 Let's solve the equation:

(3/2)x - 5/2 = 1/2

Add 5/2 to both sides:

(3/2)x = 1/2 + 5/2

(3/2)x = 6/2

(3/2)x = 3

Multiply both sides by 2/3:

x = 3 × (2/3)

x = 2

Explanation

Let's denote the number as x. According to the problem:

45 = 0.72x

To find x, divide both sides by 0.72:

x = 45 / 0.72

x = 62.5

Explanation

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

A = 4 × π × r²

Given A = 616 m², let's solve for r:

616 = 4 × π × r²

616 = 4 × (22/7) × r²

616 = 88/7 × r²

r² = 616 × 7 / 88

r² = 49

r = √49

r = 7