6500+ Quantitative Aptitude Questions and Answers With Explanation

Q:

A cube is inscribed in a sphere. A right circular cylinder is within the cube touching all the vertical faces. A right circular once is inside the cylinder. Their heights are same and the diameter of the cone is equal to that of the cylinder.

What is the ratio of the volume of the sphere to that of cone?

A) 6√3:1	B) 7 : 2
C) 3√3:1	D) 5√3:1

Answer & Explanation Answer: A) 6√3:1

Explanation:

The top view of the given assembly will look like the figure above

Outermost is the sphere. Inside that there is a cube and within that there is a cone and cylinder with same radius.

Here side of cube = a

Diameter of Sphere = body diagnol = √3 a

Radius of sphere = √3 a/2 =r1

Height of Cylinder = Height of cone = side of cube = a =h

Radius of cylinder = Radius of cone = side of cube/2 = a/2 =r2(as shown in the figure)

Volume of sphere/volume of cone =

\frac{\frac{4}{3} {πr}_{1}^{3}}{\frac{1}{3} {πr}_{2}^{2} h}

= 6√3:1

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Filed Under: Volume and Surface Area
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Q:

A solid right circular cone of radius 4 cm and height 7 cm is put inside a cylindrical vessel of radius 5 cm and height 8 cm. How much water in cubic cm will be required to fill the cylindrical vessel completely?

A) 1022.48 cubic cms	B) 1533.72 cubic cms
C) 511.24 cubic cms	D) 255.62 cubic cms

Answer & Explanation Answer: C) 511.24 cubic cms

Explanation:

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Filed Under: Area
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Q:

Select the odd number from the given alternatives.

A) 121	B) 44
C) 66	D) 111

Answer & Explanation Answer: D) 111

Explanation:

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Filed Under: Odd Man Out
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Q:

What is the simplified value of $\sqrt{\frac{{(0.07)}^{2} + {(0.29)}^{2} - 0.0203}{{(0.07)}^{3} + {(0.29)}^{3}}}$

A) 0.6	B) 0.06
C) 1/0.6	D) 1/0.06

Answer & Explanation Answer: C) 1/0.6

Explanation:

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Filed Under: Simplification
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Q:

Three triangles are marked out of a bigger triangle at the three vertices such that each side of each of the smaller triangles is one-fourth as long as each corresponding side of the bigger triangle. The ratio of the area of the three small triangles taken together to that of the rest of the bigger triangle is

A) 4 : 15	B) 3 : 13
C) 3 : 16	D) 1 : 5

Answer & Explanation Answer: B) 3 : 13

Explanation:

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Filed Under: Ratios and Proportions
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Q:

ABCD is an isosceles trapezium such that AD||BC, AB = 5 cm, AD = 8 cm and BC = 14 cm. What is the area (in cm2) of trapezium?

A) 36	B) 44
C) 88	D) 144

Answer & Explanation Answer: B) 44

Explanation:

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Filed Under: Volume and Surface Area
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Q:

$∆ DEF$ is right angled at E. If m∠F = $45^{°}$ , then find the value of (cosecD - 1/√3).

A) (√6-1)/√3	B) (1-√6)/√2
C) √3-2	D) (2-√3)/2√3

Answer & Explanation Answer: A) (√6-1)/√3

Explanation:

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Filed Under: Quantitative Aptitude - Arithmetic Ability
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Q:

The smallest number that must be subtracted from 2800 so that the obtained number is a perfect square is

A) 9	B) 69
C) 96	D) 73

Quantitative Aptitude - Arithmetic Ability Questions

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