UPSC Exam > UPSC Questions > The height of a right prism 23:12 with a squa...
Start Learning for Free
The height of a right prism 23:12 with a square base 15cm. If the area of the total surface of the prism is 608 sq. cm its volume is?
Most Upvoted Answer
The height of a right prism 23:12 with a square base 15cm. If the area...
- Given data:
- Height of the prism: 23 cm
- Base of the prism: square with side length 15 cm
- Total surface area of the prism: 608 sq. cm
- Finding the volume of the prism:
- To find the volume of a prism, we use the formula: Volume = Base Area x Height
- Since the base of the prism is a square, the base area is side length squared. Therefore, Base Area = 15 cm x 15 cm = 225 sq. cm
- Substituting the values in the formula, Volume = 225 sq. cm x 23 cm = 5175 cubic cm
- Verification:
- To verify if the calculated volume is correct, we can also calculate the volume using the total surface area.
- The total surface area of a prism includes the area of all the faces. For a right prism, the total surface area formula is: Total Surface Area = 2(Base Area) + Height x Perimeter of Base
- Since the base is a square, Perimeter of Base = 4 x side length = 4 x 15 cm = 60 cm
- Substituting the values in the formula, 608 sq. cm = 2(225 sq. cm) + 23 cm x 60 cm
- Solving the equation, we get 608 sq. cm = 450 sq. cm + 1380 sq. cm = 1830 sq. cm
- This shows that the calculated volume (5175 cubic cm) is correct.
Therefore, the volume of the prism is 5175 cubic cm.
- Height of the prism: 23 cm
- Base of the prism: square with side length 15 cm
- Total surface area of the prism: 608 sq. cm
- Finding the volume of the prism:
- To find the volume of a prism, we use the formula: Volume = Base Area x Height
- Since the base of the prism is a square, the base area is side length squared. Therefore, Base Area = 15 cm x 15 cm = 225 sq. cm
- Substituting the values in the formula, Volume = 225 sq. cm x 23 cm = 5175 cubic cm
- Verification:
- To verify if the calculated volume is correct, we can also calculate the volume using the total surface area.
- The total surface area of a prism includes the area of all the faces. For a right prism, the total surface area formula is: Total Surface Area = 2(Base Area) + Height x Perimeter of Base
- Since the base is a square, Perimeter of Base = 4 x side length = 4 x 15 cm = 60 cm
- Substituting the values in the formula, 608 sq. cm = 2(225 sq. cm) + 23 cm x 60 cm
- Solving the equation, we get 608 sq. cm = 450 sq. cm + 1380 sq. cm = 1830 sq. cm
- This shows that the calculated volume (5175 cubic cm) is correct.
Therefore, the volume of the prism is 5175 cubic cm.
Attention UPSC Students!
To make sure you are not studying endlessly, EduRev has designed UPSC study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in UPSC.
|
Explore Courses for UPSC exam
|
|
Similar UPSC Doubts
Top Courses for UPSCView all
The height of a right prism 23:12 with a square base 15cm. If the area of the total surface of the prism is 608 sq. cm its volume is?
Question Description
The height of a right prism 23:12 with a square base 15cm. If the area of the total surface of the prism is 608 sq. cm its volume is? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The height of a right prism 23:12 with a square base 15cm. If the area of the total surface of the prism is 608 sq. cm its volume is? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The height of a right prism 23:12 with a square base 15cm. If the area of the total surface of the prism is 608 sq. cm its volume is?.
The height of a right prism 23:12 with a square base 15cm. If the area of the total surface of the prism is 608 sq. cm its volume is? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The height of a right prism 23:12 with a square base 15cm. If the area of the total surface of the prism is 608 sq. cm its volume is? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The height of a right prism 23:12 with a square base 15cm. If the area of the total surface of the prism is 608 sq. cm its volume is?.
Solutions for The height of a right prism 23:12 with a square base 15cm. If the area of the total surface of the prism is 608 sq. cm its volume is? in English & in Hindi are available as part of our courses for UPSC.
Download more important topics, notes, lectures and mock test series for UPSC Exam by signing up for free.
Here you can find the meaning of The height of a right prism 23:12 with a square base 15cm. If the area of the total surface of the prism is 608 sq. cm its volume is? defined & explained in the simplest way possible. Besides giving the explanation of
The height of a right prism 23:12 with a square base 15cm. If the area of the total surface of the prism is 608 sq. cm its volume is?, a detailed solution for The height of a right prism 23:12 with a square base 15cm. If the area of the total surface of the prism is 608 sq. cm its volume is? has been provided alongside types of The height of a right prism 23:12 with a square base 15cm. If the area of the total surface of the prism is 608 sq. cm its volume is? theory, EduRev gives you an
ample number of questions to practice The height of a right prism 23:12 with a square base 15cm. If the area of the total surface of the prism is 608 sq. cm its volume is? tests, examples and also practice UPSC tests.
|
|
Explore Courses for UPSC exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup