wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Q16. A solid cube is cut into eight equal smaller cubes. What is the ratio of the total surface area of these eight smaller cubes and the surface area of the original cube?

एक ठोस घन को आठ बराबर-बराबर छोटे घनों में काटा जाता है। इस आठ छोटे घनों के कुल पृष्ठीय क्षेत्रफल और वास्तविक घन के पृष्ठीय क्षेत्रफल का अनुपात क्या है?


A

8:1

No worries! We‘ve got your back. Try BYJU‘S free classes today!
B

4:1

No worries! We‘ve got your back. Try BYJU‘S free classes today!
C

2:1

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D

1:1

No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is C

2:1


Method I:

Let one side of the original cube = x

∴ The surface area of the original cube = 6x2

The cube is cut into eight similar cubes as shown below:

As shown in the figure, one side of the smaller cube = x/2

∴ Surface area of one smaller cube = 6(x/2)2 = 3x2/2

∴ Total surface area of 8 similar cubes = 8 × 3x2/2 = 12x2

Hence, required ratio = 12x2/6x2 = 12/6 = 2/1 or 2:1

Method II:

The cube in question is a 2×2×2 cube. Hence, there are 8 smaller cubes and all of them are corner cubes.

We know that out of the total of 6 faces every corner cube has 3 faces exposed. Thus, in case of every corner cube only half of the total surface area is exposed while being a part of the original bigger cube

Thus, required ratio = Total Surface area of 8 individual smaller cubes/Surface area of original cube = Total Surface area of one smaller cube/Exposed Surface area of one smaller cube while being a part of the original bigger cube = 2/1 or 2:1

माना कि वास्तविक घन की एक भुजा = x

वास्तविक घन का पृष्ठीय क्षेत्रफल = 6x2

आठ समान घनों में कटे वास्तविक घन को नीचे दर्शाया गया हैः

आकृति में दिखाए अनुसार, छोटे घन की एक भुजा = x/2

एक छोटे घन की पृष्ठीय क्षेत्रफल = 6(x/2)2 = 3x2/2

8 समान घनों का कुल पृष्ठीय क्षेत्रफल = 8 × 3x2/2 = 12x2

इस प्रकार, आवश्यक अनुपात = 12x2/6x2 = 12/6 = 2/1 या 2:1


flag
Suggest Corrections
thumbs-up
0
similar_icon
Similar questions
View More
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
QUANTITATIVE APTITUDE
Watch in App
Join BYJU'S Learning Program
CrossIcon