Competitive Exams : Quantitative Aptitude - Mensuration (2D/3D) (Set 7) | Concept of Maths

Question 1

A solid metallic cylinder of base radius $r$ and height $h = 3r$ is melted and recast into $n$ identical solid spheres. If the total surface area increases by 25%, find the value of $n$.

Accepted Answer

C) 3

Answer

A) 6

Answer

B) 12

Answer

D) 9

Question 2

A regular hexagon is inscribed in a circle of radius $R$. This circle is itself inscribed in an equilateral triangle. What is the ratio of the area of the equilateral triangle to the area of the regular hexagon?

Accepted Answer

B) $2 : 1$

Answer

A) $3 : 2$

Answer

C) $\sqrt{3} : 1$

Answer

D) $4 : 3$

Question 3

A right circular cone is cut into three parts by two planes parallel to the base which trisect the altitude. What is the ratio of the volumes of the top, middle, and bottom parts respectively?

Accepted Answer

D) $1 : 7 : 19$

Answer

A) $1 : 2 : 3$

Answer

B) $1 : 4 : 9$

Answer

C) $1 : 7 : 20$

Question 4

A rectangular tank of dimensions $12m imes 10m imes 8m$ is full of water. An iron cube of side 4 m is lowered into the tank. How much water spills out?

Accepted Answer

A) $64m^3$

Answer

B) $960m^3$

Answer

C) $896m^3$

Answer

D) No water spills out

Question 5

A pathway of uniform width $w$ is constructed inside a circular park of radius $R$. If the area of the pathway is half the area of the park, find the width $w$.

Accepted Answer

D) $R(1 - \frac{1}{\sqrt{2}})$

Answer

A) $R(1 - \frac{1}{2})$

Answer

B) $R(\sqrt{2} - 1)$

Answer

C) $\frac{R}{2}$

Question 6

The slant height of a right circular cone is 25 cm and its curved surface area is $550cm^2$. Find its volume. (Use $\pi = 22/7$)

Accepted Answer

B) $1232cm^3$

Answer

A) $1232cm^3$

Answer

C) $1320cm^3$

Answer

D) $1540cm^3$

Question 7

Three circles of radius 4 cm each touch each other externally. Find the area of the region enclosed between them.

Accepted Answer

C) $16\sqrt{3} - 8\pi$

Answer

A) $16\sqrt{3} - 4\pi$

Answer

B) $8\sqrt{3} - 8\pi$

Answer

D) $4\sqrt{3} - 2\pi$

Question 8

A right prism has a rhombus as its base. The diagonals of the rhombus are 16 cm and 12 cm. If the total surface area of the prism is $640cm^2$, find its height.

Accepted Answer

A) 11.2 cm

Answer

B) 12 cm

Answer

C) 10 cm

Answer

D) 14.5 cm

Question 9

If the radius of a sphere is doubled, what is the percentage increase in its volume?

Accepted Answer

C) 700%

Answer

A) 100%

Answer

B) 400%

Answer

D) 800%

Question 10

A hemispherical bowl of internal radius 9 cm contains a liquid. This liquid is to be filled into cylindrical bottles of diameter 3 cm and height 4 cm. How many bottles are required to empty the bowl?

Accepted Answer

B) 54

Answer

A) 27

Answer

C) 36

Answer

D) 48