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A large cube is formed from the material obtained by melting three smaller cubes of 3, 4 and 5 cm side. What is the ratio of the total surface areas of the smaller cubes and the large cube?
- a)2 : 1
- b)3 : 2
- c)25 : 18
- d)27 : 20
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A large cube is formed from the material obtained by melting three sma...
Volume of the large cube = (33 + 43 + 53)
= 216 cm3
Let the edge of the large cube be a.
So, a3 = 216 a = 6 cm
∴ Required ratio
= [6 × (32 + 42 + 52)]/ (6 × 62)
= 50/36 = 25 : 18
= 216 cm3
Let the edge of the large cube be a.
So, a3 = 216 a = 6 cm
∴ Required ratio
= [6 × (32 + 42 + 52)]/ (6 × 62)
= 50/36 = 25 : 18
Most Upvoted Answer
A large cube is formed from the material obtained by melting three sma...
To solve this problem, we need to find the surface area of each smaller cube and the surface area of the larger cube. Then we can calculate the ratio of the total surface areas.
Calculating the surface area of each smaller cube:
- The surface area of a cube is given by the formula: 6 * side^2.
- For the first cube with a side length of 3 cm, its surface area is 6 * 3^2 = 6 * 9 = 54 cm^2.
- For the second cube with a side length of 4 cm, its surface area is 6 * 4^2 = 6 * 16 = 96 cm^2.
- For the third cube with a side length of 5 cm, its surface area is 6 * 5^2 = 6 * 25 = 150 cm^2.
Calculating the surface area of the larger cube:
- We know that the volume of the larger cube is equal to the sum of the volumes of the three smaller cubes.
- The volume of a cube is given by the formula: side^3.
- The volume of the larger cube is 3^3 + 4^3 + 5^3 = 27 + 64 + 125 = 216 cm^3.
- To find the side length of the larger cube, we take the cube root of the volume: ∛216 = 6 cm.
- The surface area of the larger cube is given by the formula: 6 * side^2 = 6 * 6^2 = 6 * 36 = 216 cm^2.
Calculating the ratio of the total surface areas:
- The total surface area of the smaller cubes is 54 + 96 + 150 = 300 cm^2.
- The ratio of the total surface areas is 300 : 216, which simplifies to 25 : 18.
Therefore, the correct answer is option C) 25 : 18.
Calculating the surface area of each smaller cube:
- The surface area of a cube is given by the formula: 6 * side^2.
- For the first cube with a side length of 3 cm, its surface area is 6 * 3^2 = 6 * 9 = 54 cm^2.
- For the second cube with a side length of 4 cm, its surface area is 6 * 4^2 = 6 * 16 = 96 cm^2.
- For the third cube with a side length of 5 cm, its surface area is 6 * 5^2 = 6 * 25 = 150 cm^2.
Calculating the surface area of the larger cube:
- We know that the volume of the larger cube is equal to the sum of the volumes of the three smaller cubes.
- The volume of a cube is given by the formula: side^3.
- The volume of the larger cube is 3^3 + 4^3 + 5^3 = 27 + 64 + 125 = 216 cm^3.
- To find the side length of the larger cube, we take the cube root of the volume: ∛216 = 6 cm.
- The surface area of the larger cube is given by the formula: 6 * side^2 = 6 * 6^2 = 6 * 36 = 216 cm^2.
Calculating the ratio of the total surface areas:
- The total surface area of the smaller cubes is 54 + 96 + 150 = 300 cm^2.
- The ratio of the total surface areas is 300 : 216, which simplifies to 25 : 18.
Therefore, the correct answer is option C) 25 : 18.
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A large cube is formed from the material obtained by melting three smaller cubes of 3, 4 and 5 cm side. What is the ratio of the total surface areas of the smaller cubes and the large cube?a)2 : 1b)3 : 2c)25 : 18d)27 : 20Correct answer is option 'C'. Can you explain this answer?
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