Explanation

Volume of iron =π(R2−r2)×h

=π(42−32)×21

=722​×(16−9)×21

=462cm2

Weight =10008×462​kg=3.696kg

Explanation

Step-by-step explanation:

A= 3.14 × 8^(2)

=3.14 × 64

=200.96m

Explanation

Calculation:

• Current total age = 80 years

• Three years ago, each person was 3 years younger.

• Since there are three people, the total reduction in age is $3\times 3=9$ years.

So, the total of their ages three years ago is:

$$\mathrm{<b><font\; color="\#0000ff">80</font></b>}<b><font\; color="\#0000ff">-</font></b>\mathrm{<b><font\; color="\#0000ff">9</font></b>}<b><font\; color="\#0000ff">=</font></b>\mathrm{<b><font\; color="\#0000ff">71</font></b>}\text{<b><font color="\#0000ff"> years</font></b>}$$

Explanation

Given that log10 2, log10(2x - 1), and log10(2x + 3) are in AP:

2 * log10(2x - 1) = log10 2 + log10(2x + 3)

log10(2x - 1)^2 = log10(2 * (2x + 3))

(2x - 1)^2 = 2 * (2x + 3)

4x^2 - 4x + 1 = 4x + 6

4x^2 - 8x - 5 = 0

(2x + 1)(2x - 5) = 0

2x = 5 or 2x = -1 ( rejected since 2x > 0 for log(2x-1) and log(2x+3) to be defined)

2x = 5

x = log2 5

Explanation

Let the total piece of land that he has be x hectares,

According to question, x/3 hectare land is used for strawberries, x/4 hectare for chesses, 3x/8 hectare for vegetables and 9 hectares for oats,

total land area= x

Therefore,

x = x/3 + x/4 + 3x/8 + 9,

taking x common,

1 = 1/3 + 1/4 + 3/8 + 9/x,

1 – (1/3 + 1/4 + 3/8) = 9/x,

1 – ((8 + 6 + 9)/24) = 9/x,

1 – (23/24) = 9/x,

1/24 = 9/x or x = 216 hectares

Explanation

40 men finish the work in 25 days

Total work = 40 men * 25 days = 1000 man-days

Now, 25 men will finish the work:

1000 man-days / 25 men = 40 days

Explanation

we divide the number of acres it can plow by the number of hours it takes:

2 acres / 4 hours = 0.5 acres per hour

0.5 acres per hour * 8 hours = 4 acres

Therefore, the tractor can plow 4 acres of land in 8 hours.

Explanation

Let V1​ and V2​ be two volume of cubes.

l1​ and l2​ be edges of the two cubes.

We know that,

Volume of cube V=l3

So,

⇒  V2​V1​​=l23​l13​​

⇒  18​=(l2​l1​​)3             [ Given ]

∴  l2​

Explanation

Q. What subject will start the series of lectures?

Ans: Algebra

Q. Which of the following day is a holiday?

Ans: Wednesday

Q. On which day the lecture of Physics is scheduled?

Ans: Tuesday

Explanation

The sequence of savings is:

4, 13, 22, ... with a common difference of 9.

Let's find the week when savings reach 130:

4 + (n-1)9 = 130

(n-1)9 = 126

n-1 = 14

n = 15

The savings will reach Rs 130 in the 15th week.