Quiz-1

Since they are directly proportional
\frac{L_{1}}{L_{2}}= \frac{B_{1}}{B_{2}}
\frac{12}{42} = \frac{x}{28}
X = \frac{(12\times 28)}{42}

∴ Breadth = 8

To find cost we need to find the perimeter of the square compound.
Perimeter can be found from area from the first statement
and the cost can be found from second.
So both the statements are needed.

Area of trapezium =\frac{1}{2} \times (\text{sum of parallel sides})\times  \text{distance between them}
1800= \frac{1}{2}\times (20+x)\times 30
120 - 20=x
100 = x

Given, total surface area = 321 cm²
⇒ 2Πrh + 2×Πr² = 321 cm²                  ..(1)

Also, according to question,
Total Surface Area = 2 × Curved Surface Area
⇒ 2Πrh + 2×Πr² = 2×2Πrh = 321                  ..(2)
⇒ 4Πrh = 321     ⇒ rh = \frac{321}{4 \pi}=25.54

Now, put the value of rh in equation (1), we get-
2Π×25.54 + 2Πr² = 321       ⇒ (25.54+r²) = \frac{321}{2 \pi}=51.09
⇒r² = 51.09-25.54         ⇒r = 5.05 cm

Since, rh= 25.54 cm²

⇒ h = \frac{25.54}{5.05}  = 5.05 cm

Hence, volume of book, V= Πr²h
⇒ V= Π × 5.05² × 5.05  = 404 cm³

A=kbc^{3}
300=k\times 5\times 2^{3}
K=\frac{15}{2}
Again
A= \frac{15}{2} \times 4 \times 125 = 3750

Area of parallelogram = 2 x  area of triangle
Area of parallelogram = 2\times (\frac{1}{2} \times base\times height)
= 20 x  12
= 240 cm²

Area of rectangle = length x breadth

= 13\times (13-7) = 78

Area = \frac{1}{2}\times d_{1}\times d_{2}
= \frac{1}{2}\times 16\times 24 cm²
= 192 cm²

Let length be 2x and breadth be x
2(2x+x) = 162

⇒ 3x = 81
breadth = x = 27

Length = 2x = 54

Area= 27 × 54
= 1458 cm²

2 km =2000 m

The number of revolution = \frac{\text{Distance covered}}{\text{Circumference of tyre}}
Number of revolutions= \frac{2000}{200}
= 10