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A trapezium based prism with two parallel sides 8 cm and 14 cm respectively and distance between two parallel sides is 8 cm. Find the height of the prism if the volume of the prism is 1056 ?
- a)11 cm
- b)10 cm
- c)9 cm
- d)12 cm
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
A trapezium based prism with two parallel sides 8 cm and 14 cm respect...
Volume of prism = (Base area) × height.
Base Area = Area of trapezium
= 1/2(8 + 14) × 8 = 88
∴ 1056 = 88 × height
Base Area = Area of trapezium
= 1/2(8 + 14) × 8 = 88
∴ 1056 = 88 × height
Most Upvoted Answer
A trapezium based prism with two parallel sides 8 cm and 14 cm respect...
To find the height of the prism, we need to use the formula for the volume of a prism. The volume of a prism is given by the formula:
Volume = Base Area x Height
Given that the volume of the prism is 1056 and the base is a trapezium with parallel sides measuring 8 cm and 14 cm, we can find the height of the prism.
Let's solve it step by step:
1. Identify the given information:
- Parallel sides of the trapezium base: 8 cm and 14 cm
- Distance between the parallel sides: 8 cm
- Volume of the prism: 1056 cm³
2. Determine the base area of the prism:
The base area of a trapezium is given by the formula:
Base Area = (a + b) / 2 * h
where a and b are the lengths of the parallel sides and h is the height of the trapezium.
In this case, a = 8 cm, b = 14 cm, and h is the height of the trapezium. We need to find the height of the trapezium to calculate the base area.
3. Find the height of the trapezium:
To find the height of the trapezium, we can use the formula for the area of a trapezium:
Area = (a + b) / 2 * h
Rearrange the formula to solve for h:
h = 2 * Area / (a + b)
In this case, the area of the base is the same as the base area of the prism, so we can substitute the values:
h = 2 * Base Area / (a + b)
4. Substitute the given values and calculate the base area:
Base Area = (8 + 14) / 2 * h
Base Area = 22 / 2 * h
Base Area = 11 * h
5. Substitute the base area into the volume formula and solve for the height:
Volume = Base Area * Height
1056 = 11 * h * Height
1056 = 11h²
Divide both sides by 11:
96 = h²
Take the square root of both sides:
√96 = h
Simplify:
h ≈ 9.8 cm
Therefore, the height of the prism is approximately 9.8 cm.
Volume = Base Area x Height
Given that the volume of the prism is 1056 and the base is a trapezium with parallel sides measuring 8 cm and 14 cm, we can find the height of the prism.
Let's solve it step by step:
1. Identify the given information:
- Parallel sides of the trapezium base: 8 cm and 14 cm
- Distance between the parallel sides: 8 cm
- Volume of the prism: 1056 cm³
2. Determine the base area of the prism:
The base area of a trapezium is given by the formula:
Base Area = (a + b) / 2 * h
where a and b are the lengths of the parallel sides and h is the height of the trapezium.
In this case, a = 8 cm, b = 14 cm, and h is the height of the trapezium. We need to find the height of the trapezium to calculate the base area.
3. Find the height of the trapezium:
To find the height of the trapezium, we can use the formula for the area of a trapezium:
Area = (a + b) / 2 * h
Rearrange the formula to solve for h:
h = 2 * Area / (a + b)
In this case, the area of the base is the same as the base area of the prism, so we can substitute the values:
h = 2 * Base Area / (a + b)
4. Substitute the given values and calculate the base area:
Base Area = (8 + 14) / 2 * h
Base Area = 22 / 2 * h
Base Area = 11 * h
5. Substitute the base area into the volume formula and solve for the height:
Volume = Base Area * Height
1056 = 11 * h * Height
1056 = 11h²
Divide both sides by 11:
96 = h²
Take the square root of both sides:
√96 = h
Simplify:
h ≈ 9.8 cm
Therefore, the height of the prism is approximately 9.8 cm.
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A trapezium based prism with two parallel sides 8 cm and 14 cm respectively and distance between two parallel sides is 8 cm. Find the height of the prism if the volume of the prism is 1056 ?a)11 cmb)10 cmc)9 cmd)12 cmCorrect answer is option 'D'. Can you explain this answer?
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A trapezium based prism with two parallel sides 8 cm and 14 cm respectively and distance between two parallel sides is 8 cm. Find the height of the prism if the volume of the prism is 1056 ?a)11 cmb)10 cmc)9 cmd)12 cmCorrect answer is option 'D'. Can you explain this answer? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about A trapezium based prism with two parallel sides 8 cm and 14 cm respectively and distance between two parallel sides is 8 cm. Find the height of the prism if the volume of the prism is 1056 ?a)11 cmb)10 cmc)9 cmd)12 cmCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A trapezium based prism with two parallel sides 8 cm and 14 cm respectively and distance between two parallel sides is 8 cm. Find the height of the prism if the volume of the prism is 1056 ?a)11 cmb)10 cmc)9 cmd)12 cmCorrect answer is option 'D'. Can you explain this answer?.
A trapezium based prism with two parallel sides 8 cm and 14 cm respectively and distance between two parallel sides is 8 cm. Find the height of the prism if the volume of the prism is 1056 ?a)11 cmb)10 cmc)9 cmd)12 cmCorrect answer is option 'D'. Can you explain this answer? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about A trapezium based prism with two parallel sides 8 cm and 14 cm respectively and distance between two parallel sides is 8 cm. Find the height of the prism if the volume of the prism is 1056 ?a)11 cmb)10 cmc)9 cmd)12 cmCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A trapezium based prism with two parallel sides 8 cm and 14 cm respectively and distance between two parallel sides is 8 cm. Find the height of the prism if the volume of the prism is 1056 ?a)11 cmb)10 cmc)9 cmd)12 cmCorrect answer is option 'D'. Can you explain this answer?.
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A trapezium based prism with two parallel sides 8 cm and 14 cm respectively and distance between two parallel sides is 8 cm. Find the height of the prism if the volume of the prism is 1056 ?a)11 cmb)10 cmc)9 cmd)12 cmCorrect answer is option 'D'. Can you explain this answer?, a detailed solution for A trapezium based prism with two parallel sides 8 cm and 14 cm respectively and distance between two parallel sides is 8 cm. Find the height of the prism if the volume of the prism is 1056 ?a)11 cmb)10 cmc)9 cmd)12 cmCorrect answer is option 'D'. Can you explain this answer? has been provided alongside types of A trapezium based prism with two parallel sides 8 cm and 14 cm respectively and distance between two parallel sides is 8 cm. Find the height of the prism if the volume of the prism is 1056 ?a)11 cmb)10 cmc)9 cmd)12 cmCorrect answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
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