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A cube whose edge is 20 cm long has circle on each of its faces painted black. What is the totalarea of the unpainted surface of the cube if the circles are of the largest area possible?
- a)85.71 cm2
- b)257.14 cm2
- c)514.28 cm2
- d)331.33 cm2
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
A cube whose edge is 20 cm long has circle on each of its faces painte...
Surface area of the cube = 6a2 = 6 × (20)2
= 2400
Area of 6 circles of radius 10 cm = 6pr2
= 6 × p × 100
= 1885.71
Remaining area = 2400 – 1884 = 514.28
= 2400
Area of 6 circles of radius 10 cm = 6pr2
= 6 × p × 100
= 1885.71
Remaining area = 2400 – 1884 = 514.28
Most Upvoted Answer
A cube whose edge is 20 cm long has circle on each of its faces painte...
Problem: Finding the area of the unpainted surface of a cube whose edges are 20 cm long and circles on each of its faces are painted black. The circles are of the largest area possible.
Solution:
Given, the edge of the cube is 20 cm.
The circle on each face of the cube is of the largest area possible.
Let the radius of the circle be 'r'.
Area of the circle = πr²
The diameter of the circle is equal to the edge of the cube.
∴ 2r = 20 cm
∴ r = 10 cm
Area of the circle on each face = π(10)² = 100π cm²
The cube has 6 faces, and each face has a painted circle.
∴ Total area of the painted circles = 6 × 100π = 600π cm²
The area of one face of the cube = (20)² = 400 cm²
The cube has 6 faces.
∴ Total area of the cube = 6 × 400 = 2400 cm²
The area of the unpainted surface of the cube = Total area of the cube - Total area of the painted circles
= 2400 - 600π cm²
= 514.28 cm² (approx)
Hence, the area of the unpainted surface of the cube is 514.28 cm².
Therefore, the correct option is (c) 514.28 cm².
Solution:
Given, the edge of the cube is 20 cm.
The circle on each face of the cube is of the largest area possible.
Let the radius of the circle be 'r'.
Area of the circle = πr²
The diameter of the circle is equal to the edge of the cube.
∴ 2r = 20 cm
∴ r = 10 cm
Area of the circle on each face = π(10)² = 100π cm²
The cube has 6 faces, and each face has a painted circle.
∴ Total area of the painted circles = 6 × 100π = 600π cm²
The area of one face of the cube = (20)² = 400 cm²
The cube has 6 faces.
∴ Total area of the cube = 6 × 400 = 2400 cm²
The area of the unpainted surface of the cube = Total area of the cube - Total area of the painted circles
= 2400 - 600π cm²
= 514.28 cm² (approx)
Hence, the area of the unpainted surface of the cube is 514.28 cm².
Therefore, the correct option is (c) 514.28 cm².
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A cube whose edge is 20 cm long has circle on each of its faces painted black. What is the totalarea of the unpainted surface of the cube if the circles are of the largest area possible?a)85.71 cm2b)257.14 cm2c)514.28 cm2d)331.33 cm2Correct answer is option 'C'. Can you explain this answer? for Quant 2026 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about A cube whose edge is 20 cm long has circle on each of its faces painted black. What is the totalarea of the unpainted surface of the cube if the circles are of the largest area possible?a)85.71 cm2b)257.14 cm2c)514.28 cm2d)331.33 cm2Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Quant 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cube whose edge is 20 cm long has circle on each of its faces painted black. What is the totalarea of the unpainted surface of the cube if the circles are of the largest area possible?a)85.71 cm2b)257.14 cm2c)514.28 cm2d)331.33 cm2Correct answer is option 'C'. Can you explain this answer?.
A cube whose edge is 20 cm long has circle on each of its faces painted black. What is the totalarea of the unpainted surface of the cube if the circles are of the largest area possible?a)85.71 cm2b)257.14 cm2c)514.28 cm2d)331.33 cm2Correct answer is option 'C'. Can you explain this answer? for Quant 2026 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about A cube whose edge is 20 cm long has circle on each of its faces painted black. What is the totalarea of the unpainted surface of the cube if the circles are of the largest area possible?a)85.71 cm2b)257.14 cm2c)514.28 cm2d)331.33 cm2Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Quant 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cube whose edge is 20 cm long has circle on each of its faces painted black. What is the totalarea of the unpainted surface of the cube if the circles are of the largest area possible?a)85.71 cm2b)257.14 cm2c)514.28 cm2d)331.33 cm2Correct answer is option 'C'. Can you explain this answer?.
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