Mu Sigma Geometry Quiz-1

As we can see 1 mm^2 is mm*mm i.e. 1m^2 can be written as 1m*1m as 1000mm*1000mm i.e.

(1000*1000)/40=25000 gives the number of meshes in a wire gauge.

We have, area of a square = 12800 sq miles.

Hence side2 = 12800

Side = √12800

⇒ Side = 80√2

We know that diagonal of a square = √2 × side

= √2 × 80√2

= 160 miles.

Hence we know that speed = distance/time

Time = distance/speed

Time = 160/15

= 10.66 miles/hr.

Volume of cone = (1/3)πr2h

Where r = radius of cone

Volume of sphere = (4/3)πR3

Where R = radius of sphere

According to the question

R = r and

(1/3)πr2h = (4/3)πR3

⇒ h = 4 × R = 2 × D (∵ 2× R = diameter of sphere = D)

⇒ h/D = 2/1

Perimeter of square = 4 × side

Perimeter of rectangle = 2 × (length + breadth)

Given

Length of rectangle = 12 cm

Perimeter of the square = 72 cm

∴ Side of square = perimeter of square /4 = 72/4

= 18 cm

According to the question

Perimeter of square = 2 × perimeter of rectangle

∴ Perimeter of rectangle = perimeter of square /2 = 72/2

⇒ 36 cm = 2 (length + breadth)

⇒ 2 × (12 +breadth) = 36 (∵ length = 12 cm)

⇒ Breadth = 6 cm

∴ Difference between side of square and breadth of rectangle = 18 – 6 = 12 cm

So the correct option is (2).

Revolutions by a wheel = Distance covered / Circumference

Circumference of wheel = Perimeter of wheel

According to question

Revolutions by front wheel - Revolutions by back wheel = 10

⇒ (Distance covered / Circumference of front wheel) - (Distance covered / Circumference of back wheel) = 10

⇒ (Distance Covered ) { (1 / Circumference of front wheel ) - (1 / Circumference of back wheel)} = 10

⇒ (Distance Covered ) { (1 / 7 ) - (1 / 9)} = 10

⇒ (Distance Covered ) { (2 /63 ) } = 10

⇒ (Distance Covered ) = 630 / 2 = 315

Revolutions by a wheel = Distance covered / Circumference

Circumference of wheel = Perimeter of wheel

Revolutions by front wheel = (Distance covered / Circumference of front wheel)

240 =Distance / 30

Distance = 7200

Revolutions by back wheel = (Distance covered / Circumference of back wheel)

Revolutions = 7200 / 20 = 360

Let the square be of Length = a

For Inner Circle the diameter of the circle = length of the side of the square = a

Dia(innner) = a

For Outer Circle the diameter of the circle = length of the Diagonal of the square = a2‾√

Dia (outer) = a2‾√

Area of a circle = (πd^2/4)

Ratio of Area of 2 Circles

Area Outer / Area Inner = (douter)^2 /(dinner)^2 = (a√2)^2 /(a)^2 = 2 / 1

Area Inner : Area Outer = 1 : 2

The wooden cube of minimum size that is to be made from blocks of 5 × 10 × 20 has a side length equal to the least common multiple (LCM) of (5, 10, 20)

LCM of (5, 10, 20) = 20

Hence, Size of Wooden block = 20cm

Volume of cubical wooden block = (size)3

∴ Volume of minimum wooden cube = 20 × 20 × 20 cm3

∵ Volume of cuboid = length × breadth × height

∴ Number of wooden blocks required = (20 × 20 × 20)/(5 × 10 × 20)

= 8 blocks

Consider the top city, the following are the 3 routes possible, starting from the leftmost edge. Since there are 3 edges emanating from each city and the figure is perfectly symmetrical, these 3 routes are possible from each edge, hence for any given city, the total number of routes = 4 * 3 = 12.

The volume of the cylinder is Pi x r^2 x h = Pi x 3^2 x 6 = 54Pi
Volume of a cylinder is 4/3 x Pi x r^3
Now 54Pi = 12 x 4/3 x Pi x r^3
54 = 16 x r^3
r^3 = 54/16 = 27/8
r = 3/2
Therefore diameter is 3 cms