SNAP Geometry Questions

Volume of one sphere = $$\frac{4}{3}\pi R^3$$ = $$36\pi$$
Volume of five spheres = $$180\pi $$
Therefore, volume of cylinder = $$180\pi $$
Radius of cylinder = 3 cm
$$\pi R^2H$$ = $$180\pi $$
H = 20 cm
Hence, option B is the correct answer.

Centroid = $$(\frac{x_{1}+x_{2}+x_{3}}{3} , \frac{y_{1}+y_{2}+y_{3}}{3})$$

(3, 2) = $$(\frac{x+4-1}{3} , \frac{1+6+y}{3})$$

$$\frac{x+3}{3}$$ = 3 and $$\frac{7+y}{3}$$ = 2

x+3 = 9 and 7+y = 6

x = 6 and y = -1

x+y = 6-1 = 5

So the answer is option C.

We know that in an equilateral triangle, centroid, orthocentre, circumcentre, and incentre are all the same point. Let’s assume O is this point for triangle ABC.
So, AD is perpendicular to BC and bisects it as well. Also, O divides AD in the ratio 2:1.
=> $$AD^2 = AC^2 - DC^2 = 36-9 = 27$$.
So, $$AD=3\sqrt{3}$$
Since, O divides AD in the ratio 2:1, AO will be $$2\sqrt{3}$$ which is the radius of the circle.
Thus, D is the correct answer.

Let r and h be the radius and height of the cone.
Initial volume = $$\frac{1}{3}*\pi*r^2*h$$
Final volume = $$\frac{1}{3}*\pi*(1.1r)^2*(1.2h)$$
Therefore, final volume = $$1.452*\frac{1}{3}*\pi*r^2*h$$
Therefore, percentage increase = $$\frac{1.452*\frac{1}{3}*\pi*r^2*h - \frac{1}{3}*\pi*r^2*h}{\frac{1}{3}*\pi*r^2*h}*100 = 45.20$$%
Hence option D is the correct answer.

The area of the circle is 616.
So, the radius of the circle is $$\sqrt{\frac{616}{\pi}}=14$$
Hence, the length of the rectangle is 14*2=28 and the breadth equals 14
So, the area of the rectangle is 14*28=392 sq m

Let us assume that the radius of the circle is r cm and the side of the triangle ABE is a cm.

Then, side of triangle ABE,

$$\Rightarrow$$ $$r$$ = $$\frac{\triangle}{S}$$   (Where $$\triangle$$ = Area of triangle and S = semi-perimeter of triangle)

$$\Rightarrow$$ $$r = \frac{(\frac{\sqrt{3}}{4})\times a^2}{\frac{3a}{2}}$$ 

$$\Rightarrow$$ $$r = \frac{a}{2\sqrt{3}}$$ 

$$\Rightarrow$$ $$a = 2\sqrt{3}\times r$$ 

We are given that the area of square ABCD = 300 sq. cm.

$$\Rightarrow$$    $$a^2 = (2\sqrt{3}\times r)^2$$

$$\Rightarrow$$    $$300 = 12r^2$$

$$\Rightarrow$$    $$r = 5 cm$$

Hence, option C is the correct answer.