Explanation

The radius can be found using the formula Circumference = 2𝜋𝑟.

Solving for 𝑟 gives 𝑟 = 308/2𝜋 ≈49 meters.

Explanation

we use the formula:

$$\text{Total Surface Area}=2\pi r(h+r)$$

Where:

• $r$ is the radius of the cylinder.
• $\mathrm{<span\; style="font-family:\; Overpass,\; sans-serif;\; font-size:\; 0.875rem;"><font\; color="\#0000ff">h\; is\; the\; height\; of\; the\; cylinder.</font></span>}$

• Radius $r = 3.5 , text{cm}$
• Height $h = 5.5 , text{cm}$

1. Plug values into the formula:
   $$\text{Total Surface Area}=2\pi \times 3.5\times (5.5+3.5)$$ $$= 2pi times 3.5 times 9$$=2×3.1416×3.5×9
   =2×3.1416×31.5
   =6.2832×31.5
   ≈198.0cm2

Explanation

Explanation

Area of the rectangular floor = Length x Width = 18 feet x 10 feet = 180 square feet

Since there are 9 square feet in a square yard, the area in square yards is:

180 square feet / 9 = 20 square yards

The cost of carpeting = Area x Rate = 20 square yards x x Rs/Sq Yard

So, the cost of carpeting is: 20x

Explanation

The mode is the value that appears most frequently in a data set.

Mode = L + (f 1– f 0/2f 1– f 0– f 2 ) h.

Explanation

In a Geometric Progression, the nth term is given by:

Tn​=a×r^n−1

Where:

• a = first term

• r = common ratio

• n = term number

Explanation

The result of the expression $4^3 - frac{4^2}{2^2}$ is 60. ​

Explanation

The study of triangles is called trigonometry.

This branch of mathematics focuses on the relationships between the angles and sides of triangles, particularly right-angled triangles

Explanation

Let the circumference of the circle = perimeter of the square = P  

- Circumference of circle = 2πr  

- Perimeter of square = 4a (a = side of square)  

So, 2πr = 4a ⇒ a = (πr)/2

- Area of circle = πr²  

- Area of square = a² = (πr/2)² = (π²r²)/4

Now compare:

πr² (circle) vs. (π²r²)/4 (square)  

Divide both sides:  

(πr²) / ((π²r²)/4) = 4/π > 1 ⇒ area of circle > area of square.

Explanation

The set $left{frac{p}{q} : p, q in mathbb{Z}, q neq 0right}$ represents the set of rational numbers.

Rational Numbers: A number is considered rational if expressed as the quotient $frac{p}{q}$, where $p$ and $q$ are integers and $q\mathrm{\ne }0$

This set includes numbers like $frac{1}{2}$, $-frac{3}{4}$, and $7$ (which can be written as $frac{7}{1}$).