With no wastage, small cubes of side 3 inches are formed from a cuboid with th

Sail E0 Webinar

Question

With no wastage, small cubes of side 3 inches are formed from a cuboid with the dimensions 2:3:9 are formed. Find the ratio of the body diagonal of the cuboid to that of all of the cubes.

Options:

A . 1:3

B . Ratio =

\frac{\sqrt{94}}{6 a^{2} 3 \sqrt{3}}

C . Ratio =

\frac{\sqrt{65 a}}{23}

D . none of these

Answer: Option B
:
B

Number of cubes = $\frac{2 a \times 3 a \times 9 a}{3 \times 3 \times 3}$ = 2a $^{3}$
Diagonal of a cube = $\sqrt{4 a^{2} + 9 a^{2} + 81 a^{2}}$
Sum of the diagonals of cubes = 2a $^{3}$ $\times$ 3 $\sqrt{3}$
Ratio = $\frac{\sqrt{4 a^{2} + 9 a^{2} + 81 a^{2}}}{2 a^{3} \times 3 \sqrt{3}}$

Was this answer helpful ?

Next Question

Submit Solution

More Questions on This Topic :

Question 1. Suresh is standing on vertex A of triangle ABC, with AB = 3, BC = 5, and CA = 4. Suresh walks according to the following....forever. What is the total distance that Suresh walks?

Question 2. All five faces of a regular pyramid with a square base are found to be of the same area. The height of the pyramid is ....is the minimum total area (integral) of all its surfaces?

Question 3. In the quadrilateral ABCD, AD = DC = CB, and ADC = 100∘, ABC = 130∘. Then the measure of ACB is &#....ABC = 130∘. Then the measure of ACB is

Question 4. An isosceles right triangle is inscribed in a square. Its hypotenuse is a mid segment of the square. What is the ratio o....ratio of the square’s area to the triangle’s area?

Question 5. Two travelers start walking from the same point at an angle of 1500 with each other at the rate of 4 kmph and 3 kmph. ....3 kmph. Find the distance between them after 2 hours

Question 6. Find the distance between the incentre and the circumcentre of a triangle with circumradius 6 and inradius 2? ....

Question 7. ΔABC is an equilateral triangle of side 14 cm. A semi circle on BC as diameter is drawn to meet AB at D, and AC at E. F....AC at E. Find the area of the shaded region?

Question 8. Four identical circles are drawn taking the vertices of a square as centers. The circles are tangential to one another. ....lying within the square to that of the smaller circle?

Question 9. In the figure given below, ABOP is a rectangle and O is the centre of the circle. It is also given that AB = BC and the ....ABC is 60∘. Findthe measure of the angle OPN.

Question 10. All sides of a regular pentagon are extended to form a star with vertices P,Q,R,S,T. What is the sum of the angles made ....is the sum of the angles made at the vertices?___

Chapter 1 - GLOBAL STEEL SCENARIO & INDIAN STEEL INDUSTRY Part 1 : (13-04-2024) INDUSTRY AND COMPANY AWARENESS (ICA)

Direction Sense Test Part 1 Reasoning (Hindi)

Chapter 1 - RMHP / OHP / OB & BP Part 1 : (14-02-2024) GPOE

Cube & Cuboid Part 1 Reasoning (Hindi)

Data Interpretation (DI) Basic Concept Reasoning (Hindi)

Counting Figures Part 1 Counting Of Straight Lines Reasoning (Hindi)

Sail E0 free webinar Webinars

Real Numbers Part 7 Class 10 Maths

Real Numbers Part 1 Class 10 Maths

Polynomials Part 1 Class 10 Maths

DSP Combined 1 Free Revision Test SAIL JO E-0

GPOE / GPA Combined 1 Free Revision Test SAIL JO E-0

BSP Plant Specific Review Test SAIL JO E-0

BSL Combined 1 Free Revision Test SAIL JO E-0

GFM Combined 1 Free Revision Test SAIL JO E-0