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

We are told:

Average of 5 numbers = 34

Total sum of 5 numbers = 34 × 5 = 170

Given 3 numbers: 28, 30, 32

Sum of these = 28 + 30 + 32 = 90

Remaining sum = 170 - 90 = 80

Remaining numbers = 2

Average of remaining = 80 ÷ 2 = 40

Explanation

The mixture contains 12% copper, which means that 12% of the mixture's weight is copper.

We want to find out how many kg of mixture is required to get 69 kg of copper.

Let's say the weight of the mixture is x kg.

Since 12% of the mixture is copper, the weight of copper in the mixture is 12% of x, which is 0.12x.

We are told that the weight of copper is 69 kg, so we can set up the equation:

0.12x = 69

To solve for x, we can divide both sides by 0.12:

x = 69 / 0.12

x = 575

So, the weight of the mixture is 575 kg.

Explanation

If the average yield per hectare for a specific crop is 500 kilograms and a farmer has a field of 2 hectares, the total yield can be calculated by multiplying the average yield per hectare by the number of hectares:

Total yield = Average yield per hectare × Number of hectares

              = 500 kilograms/hectare × 2 hectares

              = 1000 kilograms

So, the total yield from the farmer's field would be 1000 kilograms.

Explanation

Total of 3 ages = 17 + 16 + 12 = 45

New average = 20, for 4 people → Total = 20 × 4 = 80

Age of 4th person = 80 − 45 = 35

Explanation

 We are given:

• 6 kangaroos eat 6 bags in 6 days

We are asked:
How many kangaroos will eat 100 bags in 100 days?

Step 1: Understand the rate

From the first statement:

6 kangaroos eat 6 bags in 6 days.
So, 1 kangaroo eats 1 bag in 6 days.

Therefore, in 1 day, 1 kangaroo eats 1/6 of a bag.

So, in 100 days, 1 kangaroo eats:

Now, let N be the number of kangaroos needed to eat 100 bags in 100 days.

If each kangaroo eats $frac{100}{6}$/6bags in 100 days, then:

Explanation

The average of the first n natural numbers is given by (n + 1) / 2.

For n = 97:

Average = (97 + 1) / 2

= 98 / 2

= 49

Explanation

Let the total distance be x km.

The man covers half the distance at 6 km/hr, so the time taken to cover this half is:

Time = Distance / Speed = (x/2) / 6 = x/12

The man covers the remaining half at 3 km/hr, so the time taken to cover this half is:

Time = Distance / Speed = (x/2) / 3 = x/6

The total time taken to cover the entire distance is the sum of the times taken to cover each half:

Total Time = x/12 + x/6

To add these fractions, we need a common denominator, which is 12. So we can rewrite the fractions as:

Total Time = x/12 + 2x/12 = 3x/12 = x/4

Now, we can find the average speed:

Average Speed = Total Distance / Total Time = x / (x/4) = 4 km/hr

So, the correct answer is: 4 km/hr

Explanation

 To find the price of 7 toys if 1 toy costs 31:

Total Price=31×7=217

Explanation