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The base of a right prism is a trapezium whose parallel sides are 11 cm and 15 cm and the distance between them is 9 cm. If the volume of the prism is 1614.6 cm3, then the height (in cm) of the prism is:
- a)13.8
- b)12.6
- c)14.2
- d)15.5
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
The base of a right prism is a trapezium whose parallel sides are 11 c...
To find the height of the prism, we first need to calculate the area of the trapezium base. Then, we can use the formula for the volume of a prism to solve for the height.
Finding the area of the trapezium base:
The formula for the area of a trapezium is A = (a + b) * h / 2, where a and b are the lengths of the parallel sides and h is the distance between them.
Given:
a = 11 cm (length of one parallel side)
b = 15 cm (length of the other parallel side)
h = 9 cm (distance between the parallel sides)
Using the formula, we can calculate the area of the trapezium:
A = (11 + 15) * 9 / 2
A = 26 * 9 / 2
A = 234 / 2
A = 117 cm²
Finding the height of the prism:
The formula for the volume of a prism is V = A * h, where A is the base area and h is the height of the prism.
Given:
V = 1614.6 cm³ (volume of the prism)
A = 117 cm² (area of the trapezium base)
Using the formula, we can solve for h:
1614.6 = 117 * h
h = 1614.6 / 117
h ≈ 13.8 cm
Therefore, the height of the prism is approximately 13.8 cm, which corresponds to option A.
Finding the area of the trapezium base:
The formula for the area of a trapezium is A = (a + b) * h / 2, where a and b are the lengths of the parallel sides and h is the distance between them.
Given:
a = 11 cm (length of one parallel side)
b = 15 cm (length of the other parallel side)
h = 9 cm (distance between the parallel sides)
Using the formula, we can calculate the area of the trapezium:
A = (11 + 15) * 9 / 2
A = 26 * 9 / 2
A = 234 / 2
A = 117 cm²
Finding the height of the prism:
The formula for the volume of a prism is V = A * h, where A is the base area and h is the height of the prism.
Given:
V = 1614.6 cm³ (volume of the prism)
A = 117 cm² (area of the trapezium base)
Using the formula, we can solve for h:
1614.6 = 117 * h
h = 1614.6 / 117
h ≈ 13.8 cm
Therefore, the height of the prism is approximately 13.8 cm, which corresponds to option A.
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Community Answer
The base of a right prism is a trapezium whose parallel sides are 11 c...
Given :
Base of the prism is trapezium parallel sides of trapezium are 11 cm and 15 cm
Height of the trapezium = 9 cm
Volume of the prism = 1614.6 cm3
Formula used :
Area of trapezium = (1/2) × (sum of parallel sides) × height ------ (1)
Volume of prism = Area of the base × height ----- (2)
Calculations :
Using equation (1), we get
Area of trapezium = (1/2) × (11 + 15) × 9
⇒ (1/2) × 26 × 9
⇒ 13 × 9
⇒ 117 cm2
Using equation (2)
Let h be the height of the prism
⇒ Volume of prism with base as trapezium = Base area of trapezium × height
⇒ 1614.6 = 117 × h
⇒ h = 1614.6/117
⇒ h = 13.8 cm
∴ The height (in cm) of the prism is 13.8 cm.
Base of the prism is trapezium parallel sides of trapezium are 11 cm and 15 cm
Height of the trapezium = 9 cm
Volume of the prism = 1614.6 cm3
Formula used :
Area of trapezium = (1/2) × (sum of parallel sides) × height ------ (1)
Volume of prism = Area of the base × height ----- (2)
Calculations :
Using equation (1), we get
Area of trapezium = (1/2) × (11 + 15) × 9
⇒ (1/2) × 26 × 9
⇒ 13 × 9
⇒ 117 cm2
Using equation (2)
Let h be the height of the prism
⇒ Volume of prism with base as trapezium = Base area of trapezium × height
⇒ 1614.6 = 117 × h
⇒ h = 1614.6/117
⇒ h = 13.8 cm
∴ The height (in cm) of the prism is 13.8 cm.
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The base of a right prism is a trapezium whose parallel sides are 11 cm and 15 cm and the distance between them is 9 cm. If the volume of the prism is 1614.6 cm3, then the height (in cm) of the prism is:a)13.8b)12.6c)14.2d)15.5Correct answer is option 'A'. Can you explain this answer?
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The base of a right prism is a trapezium whose parallel sides are 11 cm and 15 cm and the distance between them is 9 cm. If the volume of the prism is 1614.6 cm3, then the height (in cm) of the prism is:a)13.8b)12.6c)14.2d)15.5Correct answer is option 'A'. Can you explain this answer? for CTET & State TET 2024 is part of CTET & State TET preparation. The Question and answers have been prepared according to the CTET & State TET exam syllabus. Information about The base of a right prism is a trapezium whose parallel sides are 11 cm and 15 cm and the distance between them is 9 cm. If the volume of the prism is 1614.6 cm3, then the height (in cm) of the prism is:a)13.8b)12.6c)14.2d)15.5Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for CTET & State TET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The base of a right prism is a trapezium whose parallel sides are 11 cm and 15 cm and the distance between them is 9 cm. If the volume of the prism is 1614.6 cm3, then the height (in cm) of the prism is:a)13.8b)12.6c)14.2d)15.5Correct answer is option 'A'. Can you explain this answer?.
The base of a right prism is a trapezium whose parallel sides are 11 cm and 15 cm and the distance between them is 9 cm. If the volume of the prism is 1614.6 cm3, then the height (in cm) of the prism is:a)13.8b)12.6c)14.2d)15.5Correct answer is option 'A'. Can you explain this answer? for CTET & State TET 2024 is part of CTET & State TET preparation. The Question and answers have been prepared according to the CTET & State TET exam syllabus. Information about The base of a right prism is a trapezium whose parallel sides are 11 cm and 15 cm and the distance between them is 9 cm. If the volume of the prism is 1614.6 cm3, then the height (in cm) of the prism is:a)13.8b)12.6c)14.2d)15.5Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for CTET & State TET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The base of a right prism is a trapezium whose parallel sides are 11 cm and 15 cm and the distance between them is 9 cm. If the volume of the prism is 1614.6 cm3, then the height (in cm) of the prism is:a)13.8b)12.6c)14.2d)15.5Correct answer is option 'A'. Can you explain this answer?.
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