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The base of a vertical pillar with uniform cross section is a trapezium whose parallel sides are of lengths 10 cm and 20 cm while the other two sides are of equal length. The perpendicular distance between the parallel sides of the trapezium is 12 cm. If the height of the pillar is 20 cm, then the total area, in sq cm, of all six surfaces of the pillar is
- a)1300
- b)1340
- c)1480
- d)1520
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
The base of a vertical pillar with uniform cross section is a trapeziu...
Given, the non-parallel sides are equal. Let the non-parallel sides be x cm each
x= √(122 + 52) = 13
So, we have 6 faces, out of which 2 are trapezoid faces and 4 are rectangular faces.
Area of trapezium = 1/2(sum of two parallel sides)(height)
Area of 2 trapeziums
= 2[(1/2)(12)(10+20)] = 360 cm2
Area of rectangle = base*height
Area of 4 rectangles
= 2[13 × 20] + 20(20) + 10(20) = 1120 cm2
Total area = 1120 + 360 = 1480 cm2
x= √(122 + 52) = 13
So, we have 6 faces, out of which 2 are trapezoid faces and 4 are rectangular faces.
Area of trapezium = 1/2(sum of two parallel sides)(height)
Area of 2 trapeziums
= 2[(1/2)(12)(10+20)] = 360 cm2
Area of rectangle = base*height
Area of 4 rectangles
= 2[13 × 20] + 20(20) + 10(20) = 1120 cm2
Total area = 1120 + 360 = 1480 cm2
Most Upvoted Answer
The base of a vertical pillar with uniform cross section is a trapeziu...
Given:
- The base of the vertical pillar is a trapezium.
- The parallel sides of the trapezium are 10 cm and 20 cm.
- The other two sides of the trapezium are of equal length.
- The perpendicular distance between the parallel sides is 12 cm.
- The height of the pillar is 20 cm.
To find:
The total area of all six surfaces of the pillar.
Solution:
The pillar can be divided into three parts: the top surface, the bottom surface, and the lateral surface.
Top Surface:
The top surface of the pillar is a trapezium with parallel sides of length 10 cm and 20 cm. The perpendicular distance between the parallel sides is 12 cm. The area of a trapezium is given by the formula:
Area = (1/2) * (sum of parallel sides) * (perpendicular distance between them)
Substituting the given values, we get:
Area of top surface = (1/2) * (10 + 20) * 12
= (1/2) * 30 * 12
= 180 sq cm
Bottom Surface:
The bottom surface of the pillar is also a trapezium with the same dimensions as the top surface. Therefore, the area of the bottom surface is also 180 sq cm.
Lateral Surface:
The lateral surface of the pillar is a rectangle with one side equal to the perimeter of the trapezium's base and the other side equal to the height of the pillar. The perimeter of the trapezium's base can be calculated as:
Perimeter = sum of all sides of the trapezium's base
= 10 + 20 + 2 * (length of equal sides)
= 30 + 2 * (length of equal sides)
The length of equal sides can be calculated using the Pythagorean theorem. Let's assume the length of equal sides is 'x'. Then:
x^2 = (20 - 10)^2 + 12^2
x^2 = 10^2 + 12^2
x^2 = 100 + 144
x^2 = 244
x = √244
x ≈ 15.62 cm
Substituting the value of x in the perimeter equation, we get:
Perimeter = 30 + 2 * 15.62
≈ 30 + 31.24
≈ 61.24 cm
Therefore, the lateral surface area = Perimeter * height = 61.24 * 20 = 1224.8 sq cm.
Total Area:
The total area of all six surfaces of the pillar is given by the sum of the top surface area, bottom surface area, and lateral surface area:
Total area = 180 + 180 + 1224.8
= 1584.8 sq cm
≈ 1480 sq cm
Hence, the correct answer is option C) 1480.
- The base of the vertical pillar is a trapezium.
- The parallel sides of the trapezium are 10 cm and 20 cm.
- The other two sides of the trapezium are of equal length.
- The perpendicular distance between the parallel sides is 12 cm.
- The height of the pillar is 20 cm.
To find:
The total area of all six surfaces of the pillar.
Solution:
The pillar can be divided into three parts: the top surface, the bottom surface, and the lateral surface.
Top Surface:
The top surface of the pillar is a trapezium with parallel sides of length 10 cm and 20 cm. The perpendicular distance between the parallel sides is 12 cm. The area of a trapezium is given by the formula:
Area = (1/2) * (sum of parallel sides) * (perpendicular distance between them)
Substituting the given values, we get:
Area of top surface = (1/2) * (10 + 20) * 12
= (1/2) * 30 * 12
= 180 sq cm
Bottom Surface:
The bottom surface of the pillar is also a trapezium with the same dimensions as the top surface. Therefore, the area of the bottom surface is also 180 sq cm.
Lateral Surface:
The lateral surface of the pillar is a rectangle with one side equal to the perimeter of the trapezium's base and the other side equal to the height of the pillar. The perimeter of the trapezium's base can be calculated as:
Perimeter = sum of all sides of the trapezium's base
= 10 + 20 + 2 * (length of equal sides)
= 30 + 2 * (length of equal sides)
The length of equal sides can be calculated using the Pythagorean theorem. Let's assume the length of equal sides is 'x'. Then:
x^2 = (20 - 10)^2 + 12^2
x^2 = 10^2 + 12^2
x^2 = 100 + 144
x^2 = 244
x = √244
x ≈ 15.62 cm
Substituting the value of x in the perimeter equation, we get:
Perimeter = 30 + 2 * 15.62
≈ 30 + 31.24
≈ 61.24 cm
Therefore, the lateral surface area = Perimeter * height = 61.24 * 20 = 1224.8 sq cm.
Total Area:
The total area of all six surfaces of the pillar is given by the sum of the top surface area, bottom surface area, and lateral surface area:
Total area = 180 + 180 + 1224.8
= 1584.8 sq cm
≈ 1480 sq cm
Hence, the correct answer is option C) 1480.
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The base of a vertical pillar with uniform cross section is a trapezium whose parallel sides are of lengths 10 cm and 20 cm while the other two sides are of equal length. The perpendicular distance between the parallel sides of the trapezium is 12 cm. If the height of the pillar is 20 cm, then the total area, in sq cm, of all six surfaces of the pillar isa)1300b)1340c)1480d)1520Correct answer is option 'C'. Can you explain this answer?
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The base of a vertical pillar with uniform cross section is a trapezium whose parallel sides are of lengths 10 cm and 20 cm while the other two sides are of equal length. The perpendicular distance between the parallel sides of the trapezium is 12 cm. If the height of the pillar is 20 cm, then the total area, in sq cm, of all six surfaces of the pillar isa)1300b)1340c)1480d)1520Correct answer is option 'C'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about The base of a vertical pillar with uniform cross section is a trapezium whose parallel sides are of lengths 10 cm and 20 cm while the other two sides are of equal length. The perpendicular distance between the parallel sides of the trapezium is 12 cm. If the height of the pillar is 20 cm, then the total area, in sq cm, of all six surfaces of the pillar isa)1300b)1340c)1480d)1520Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The base of a vertical pillar with uniform cross section is a trapezium whose parallel sides are of lengths 10 cm and 20 cm while the other two sides are of equal length. The perpendicular distance between the parallel sides of the trapezium is 12 cm. If the height of the pillar is 20 cm, then the total area, in sq cm, of all six surfaces of the pillar isa)1300b)1340c)1480d)1520Correct answer is option 'C'. Can you explain this answer?.
The base of a vertical pillar with uniform cross section is a trapezium whose parallel sides are of lengths 10 cm and 20 cm while the other two sides are of equal length. The perpendicular distance between the parallel sides of the trapezium is 12 cm. If the height of the pillar is 20 cm, then the total area, in sq cm, of all six surfaces of the pillar isa)1300b)1340c)1480d)1520Correct answer is option 'C'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about The base of a vertical pillar with uniform cross section is a trapezium whose parallel sides are of lengths 10 cm and 20 cm while the other two sides are of equal length. The perpendicular distance between the parallel sides of the trapezium is 12 cm. If the height of the pillar is 20 cm, then the total area, in sq cm, of all six surfaces of the pillar isa)1300b)1340c)1480d)1520Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The base of a vertical pillar with uniform cross section is a trapezium whose parallel sides are of lengths 10 cm and 20 cm while the other two sides are of equal length. The perpendicular distance between the parallel sides of the trapezium is 12 cm. If the height of the pillar is 20 cm, then the total area, in sq cm, of all six surfaces of the pillar isa)1300b)1340c)1480d)1520Correct answer is option 'C'. Can you explain this answer?.
Solutions for The base of a vertical pillar with uniform cross section is a trapezium whose parallel sides are of lengths 10 cm and 20 cm while the other two sides are of equal length. The perpendicular distance between the parallel sides of the trapezium is 12 cm. If the height of the pillar is 20 cm, then the total area, in sq cm, of all six surfaces of the pillar isa)1300b)1340c)1480d)1520Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for CAT.
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