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A 5 cm cube is cut into as many 1 cm cubes as possible. What is the ratio of the surface area of the larger cube to that of the sum of the surface areas of the smaller cubes?
- a)1 : 6
- b)1 : 5
- c)1 : 25
- d)1 : 125
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
A 5 cm cube is cut into as many 1 cm cubes as possible. What is the ra...
The volume of the larger cube = 53 = 125 cm3.
The volume of each of the smaller cubes = 13 = 1 cm3. Therefore, one would get 125 smaller cubes.
The surface area of the larger cube = 6a2 = 6(52) = 6 * 25 = 150
The surface area of each of the smaller cubes = 6 (12) = 6.
Therefore, surface area of all of the 125, 1 cm3 cubes = 125 * 6 = 750.
Therefore, the required ratio = 150 : 750 = 1 : 5
The volume of each of the smaller cubes = 13 = 1 cm3. Therefore, one would get 125 smaller cubes.
The surface area of the larger cube = 6a2 = 6(52) = 6 * 25 = 150
The surface area of each of the smaller cubes = 6 (12) = 6.
Therefore, surface area of all of the 125, 1 cm3 cubes = 125 * 6 = 750.
Therefore, the required ratio = 150 : 750 = 1 : 5
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A 5 cm cube is cut into as many 1 cm cubes as possible. What is the ra...
Problem Analysis:
To solve this problem, we need to find the ratio of the surface area of the larger cube to the sum of the surface areas of the smaller cubes. We can find the surface area of the larger cube by multiplying the length of one side by the length of one side, and then multiplying that result by six (since a cube has six equal sides). To find the sum of the surface areas of the smaller cubes, we need to determine how many 1 cm cubes can fit inside the larger cube and then multiply that number by the surface area of one 1 cm cube.
Solution:
Step 1: Determine the surface area of the larger cube.
The length of one side of the larger cube is 5 cm. Therefore, the surface area of the larger cube is 5 cm * 5 cm * 6 = 150 cm².
Step 2: Determine the number of 1 cm cubes that can fit inside the larger cube.
Since the length of one side of the larger cube is 5 cm, it can be divided into 5 smaller cubes along each side. Therefore, the total number of 1 cm cubes that can fit inside the larger cube is 5 * 5 * 5 = 125.
Step 3: Determine the surface area of one 1 cm cube.
The length of one side of the smaller cube is 1 cm. Therefore, the surface area of one 1 cm cube is 1 cm * 1 cm * 6 = 6 cm².
Step 4: Determine the sum of the surface areas of the smaller cubes.
The total number of 1 cm cubes is 125. Therefore, the sum of the surface areas of the smaller cubes is 125 * 6 cm² = 750 cm².
Step 5: Determine the ratio of the surface area of the larger cube to the sum of the surface areas of the smaller cubes.
The ratio of the surface area of the larger cube to the sum of the surface areas of the smaller cubes is 150 cm² : 750 cm². Simplifying this ratio, we get 1 : 5.
Therefore, the correct answer is option B) 1 : 5.
To solve this problem, we need to find the ratio of the surface area of the larger cube to the sum of the surface areas of the smaller cubes. We can find the surface area of the larger cube by multiplying the length of one side by the length of one side, and then multiplying that result by six (since a cube has six equal sides). To find the sum of the surface areas of the smaller cubes, we need to determine how many 1 cm cubes can fit inside the larger cube and then multiply that number by the surface area of one 1 cm cube.
Solution:
Step 1: Determine the surface area of the larger cube.
The length of one side of the larger cube is 5 cm. Therefore, the surface area of the larger cube is 5 cm * 5 cm * 6 = 150 cm².
Step 2: Determine the number of 1 cm cubes that can fit inside the larger cube.
Since the length of one side of the larger cube is 5 cm, it can be divided into 5 smaller cubes along each side. Therefore, the total number of 1 cm cubes that can fit inside the larger cube is 5 * 5 * 5 = 125.
Step 3: Determine the surface area of one 1 cm cube.
The length of one side of the smaller cube is 1 cm. Therefore, the surface area of one 1 cm cube is 1 cm * 1 cm * 6 = 6 cm².
Step 4: Determine the sum of the surface areas of the smaller cubes.
The total number of 1 cm cubes is 125. Therefore, the sum of the surface areas of the smaller cubes is 125 * 6 cm² = 750 cm².
Step 5: Determine the ratio of the surface area of the larger cube to the sum of the surface areas of the smaller cubes.
The ratio of the surface area of the larger cube to the sum of the surface areas of the smaller cubes is 150 cm² : 750 cm². Simplifying this ratio, we get 1 : 5.
Therefore, the correct answer is option B) 1 : 5.
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A 5 cm cube is cut into as many 1 cm cubes as possible. What is the ratio of the surface area of the larger cube to that of the sum of the surface areas of the smaller cubes?a)1 : 6b)1 : 5c)1 : 25d)1 : 125Correct answer is option 'B'. Can you explain this answer?
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A 5 cm cube is cut into as many 1 cm cubes as possible. What is the ratio of the surface area of the larger cube to that of the sum of the surface areas of the smaller cubes?a)1 : 6b)1 : 5c)1 : 25d)1 : 125Correct answer is option 'B'. Can you explain this answer? for UPSC 2025 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A 5 cm cube is cut into as many 1 cm cubes as possible. What is the ratio of the surface area of the larger cube to that of the sum of the surface areas of the smaller cubes?a)1 : 6b)1 : 5c)1 : 25d)1 : 125Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for UPSC 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A 5 cm cube is cut into as many 1 cm cubes as possible. What is the ratio of the surface area of the larger cube to that of the sum of the surface areas of the smaller cubes?a)1 : 6b)1 : 5c)1 : 25d)1 : 125Correct answer is option 'B'. Can you explain this answer?.
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