A solid cubical block has dimension as shown in the figure and the blo

Question

https://gmatclub.com/forum/download/file.php?id=27727 A solid cubical block has dimension as shown in the figure and the block is to be cut in half as indicated be the shared region. What is the total surface area of one of the resulting halves of the block ? A. 27+9 \sqrt 2 B. 27 C. 27+ \sqrt 9 D. 28 E. 29+9 \sqrt 2 4587ans A.jpg

Bunuel · Accepted Answer

We should find the total surface area of the figure below: https://gmatclub.com/forum/download/file.php?id=42108 Notice that it has five faces: Two 3 by 3 squares. Area = 2*3^2 = 18 Two right triangles which make up one 3 by 3 square (purple face + opposite face). Area = 3^2 = 9 One face which is 3 by 3\sqrt{2} (pink face). Area = 3*3\sqrt{2}=9\sqrt{2} The total surface area = 18 + 9 + 9\sqrt{2}=27+9\sqrt{2} . Answer: A. Hope it's clear. bP5XZ.png

ENGRTOMBA2018 · Answer

What question # is this from the official guide. Which official guide is this from? Official guide or the quant review? Please mention the complete thing.

You need to find the total area of the 2 halves created by the black plane added to the figure. Doing this, you will get 6 distinct regions that will be the

1. rectangle shaded in black with dimensions 3  \sqrt(2)  * 3
2. 2 slanted rectangles with dimensions 3*3
3. 2 Triangles, 1 at the top and 1 at the bottom with area : 0.5*3*3

Thus the total surface area of the 1 of the 2 halves created: 3  \sqrt(2)  * 3 + 2*0.5*3*3 + 2*3*3 = 9+18+9  \sqrt(2)  = 27+ 9  \sqrt(2)  . A is the correct answer.

anik19890 · Answer

thank you very much. but i can not understand ``one of the resulting halves```. what does it mean to the structure?

ENGRTOMBA2018 · Answer

You still have not provided the question number of this question from the official guide.

Dividing into halves means that the shaded plane divides the cube into 2 equal shapes/halves having identical properties.

AbdurRakib · Answer

May be Typo mistake.The distinct regions will be 5.

stonecold · Answer

Here is my approach => total surface area => Area of all the surfaces 
=> 3^2+3^2+3^2 +3√18 => 27+9√2 => A is correct.

sadikabid27 · Answer

Bunuel   VeritasPrepKarishma  please share your approach. Thanks.

dave13 · Answer

Hello pushpitkc

what is the tempereture under sun today ?

i know that Surface Area of Cube is 6a^2 so plug in 3 into this formula and get 54. if cube is divided into halves then i get 54/2 = 27 so what am i missing ?

thanks

pushpitkc · Answer

Hey dave13 It has been hot and humid here

So, the total surface area of a cube is got by adding the individual areas of the 6 faces of the cube. Now, when the cube is cut in half, there are 5 individual areas that are added in order to give us the surface area of the figure formed. Diagram.png When you add the individual areas you will get the total area, which is 18 + 9 + 9\sqrt{2} = 27 + 9\sqrt{2} Hope this helps you!

dave13 · Answer

pushpitkc thanks for explanation but i just dont get why you get area of rectanle 9\sqrt{2} and area of two face 18

what faces ?

why you marked you marked some parts in red ?

and how do you get right triangle

This is how I see when cube is cut into halves. So when it is cut I see two equilateral triangles, two rectangles and bottom surface of square shape which occurred as a result of samurai cutting it into halves

surfingpirate · Answer

Still not following this. How does one get the dimensions of 3 * 3\sqrt{2} for the area of the shaded black region? @bunel

pushpitkc · Answer

Hey  dave13

One of the faces(flat surface) of the cube is a square.

Property 
If the side of the square is x, the diagonal of the square is  x\sqrt{2}

So, in the square where the length of the side is 3, the diagonal is  3\sqrt{2} 
The triangle has 3 sides -  3,3,3\sqrt{2} . This makes the triangle an isosceles
right triangle as the sides are in the ratio  1:1:\sqrt{2} (Not iscoceles)

Each of the right-angled triangle has the area of  \frac{1}{2}*  Product of the legs =  \frac{1}{2}*3*3 = 4.5 
Therefore, the sum of the areas of both the triangles will be  4.5*2 = 9

Hope this helps you!

surfingpirate  - Hope this explanation clears your confusion as well

dave13 · Answer

Bunuel , pushpitkc , hello there

thanks for great explanation:) i have one question

Regarding this part One face which is 3 by 3\sqrt{2} (pink face). Area = 3*3\sqrt{2}=9\sqrt{2} So when diagonal divides square into halves we get TWO ISOLESCES RIGHT triangles with BASE 3 and HEIGHT 3. so area one ISOLESCES RIGHT TRIANGLE IS base * heght /2 ---> 3*3/2 = 4.5 same rule applies to the second ISOLESCES RIGHT TRIANGLE So total area of pink face is 4.5+4.5 = 9 , so my question if we have found area of pink face why do we attach \sqrt{2} to 9 can you please explain the logic ? thanks and have a good weekend

Bunuel · Answer

Pink face is a RECTANGLE, which is 3 by  3\sqrt{2} .

sandman13 · Answer

Bunuel , I got this problem in a GMAT Prep test. Someone should add the tag pertaining to the question source.

bumpbot · Answer

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A solid cubical block has dimension as shown in the figure and the blo

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