Zoho Geometry and Mensuration Quiz 1

Let the angles be 17x, 3x and 10x respectively.

Sum of all angles of a triangle = 180

17x + 3x + 10x = 180

30x = 180

X = 6

Smallest angle = 3x = 18^{\circ}

Let the radius of the smaller circle = r

=> Radius of bigger circle = \frac{7r}{5}

Area of smaller circle = \pi\left ( r \right )^{2}

Area of the bigger circle = \pi\left ( \frac{7r}{5} \right )^{2}

= \pi \frac{49r^{2}}{25}

=> Ratio of area of bigger circle to that of smaller =

\frac{\pi \frac{49r^{2}}{25}}{\pi\left ( r \right )^{2}}

= \frac{49}{25}

Area of the ring ( Circular path ) = \pi (20^{2}- 7^{2})

351*\frac{22}{7}

Total cost at  rate of Rs 161 per Sq.m = 161*351*\frac{22}{7}

= 177606

Since the sides containing the right angles are 11 cm and 60 cm, the area of the triangle is 330 sq.m.

As Area =  \frac{1}{2}*base*height

Consider PR as base

Area =  \frac{1}{2}*PR*QD

As PR = 61m, we have

330 = \frac{1}{2}*61*QD

QD = 660/61 = 10.82 m (approx)

\frac{AB}{DE} = \frac{BC}{EF} = \frac{AC}{DF}

\frac{3.6}{1.8} = \frac{4.2}{EF} = \frac{AC}{1.7}

=> EF = 2.1 cm and AC = 3.4 cm

Let the starting point be O . After 6 hours Ariana will be at X, which will be 6*18 = 108 km from O.

Billie will be at Y, which will be 6*14 = 84 km from O in the direction perpendicular to OX.

Using Pythagoras theorem, we can find the third side XY as \sqrt{108^{2}+84^{2}}

= 12\sqrt{130}

Hence Ariana and Billie will be 12\sqrt{130} km from each other

Distance covered = number of revolutions * circumference of the wheel

143 = 125\times \pi d

Where d is the diameter of the wheel

=> d = \frac{143 \times 7}{125 \times 22}

= 0.364 cm

minor sector \angle AOB = 90 degree

Angle of major sector = 360 - 90 = 270

=> \frac{270}{360}\times \frac{2\times 22}{7}\times 35

= 165 cm

t^{2}= d^{2}-\left ( R-r \right )^{2}, where

t = length of direct common tangent

d = distance between their centers

R, r => radii of the two circles

d = r + R

= 4 + 5 = 9 ( As the two circles touch externally)

 

t^{2}= 9^{2}-\left ( 5-4 \right )^{2}

t = \sqrt{80}

= 4\sqrt{5} cm

Area of square = 237.16 sq.cm

=> side = 15.4 cm

Perimeter = 4 * 15.4 = 61.6 cm

This will be the circumference of the circle

[latex2 ]\frac{22}{7} r = 61.6[/latex]

r = \frac{7 \times 61.6}{44} = 9.8 cm