All Courses
Explore Courses UPSC Exam UPSC Test Series Free Notes EduRev Infinity Get the App Login Join for Free
Sign in Open App
CAT Exam  >  CAT Questions  >  Solve the following question and mark the bes... Start Learning for Free
SaveJoin the Discussion on the App
Solve the following question and mark the best possible option.
 
Q. The volume of a pyramid with a square base is 200 cm3. The height of the pyramid is 13 cm. What will be the length of the slant edges (i.e. the distance between the apex and any other vertex), rounded to the nearest integer?
  • a)
    12 cm
  • b)
    13 cm
  • c)
    14 cm
  • d)
    15 cm
  • e)
    16 cm
Correct answer is option 'C'. Can you explain this answer?
FREE This question is part of
Download PDF Attempt Test
Download PDF Attempt this Test
Verified Answer
Solve the following question and mark the best possible option.Q.The v...
View all questions of this test
Most Upvoted Answer
Solve the following question and mark the best possible option.Q.The v...
To solve the given question, we need to use the formula for the volume of a pyramid and the Pythagorean theorem.

1. Formula for the volume of a pyramid:
The volume of a pyramid is given by the formula:
V = (1/3) * base_area * height

2. Given information:
Volume of the pyramid = 200 cm^3
Height of the pyramid = 13 cm

3. Finding the base area:
From the given information, we can rearrange the formula for the volume of a pyramid to solve for the base area:
base_area = (3 * V) / height

Plugging in the values, we get:
base_area = (3 * 200) / 13
base_area = 600 / 13
base_area ≈ 46.15 cm^2

4. Finding the length of the slant edges:
In a pyramid with a square base, the slant edge is the hypotenuse of a right-angled triangle, where the base and height of the triangle are equal to the sides of the square base.

Let's assume the length of each side of the square base is 's'. Then, using the Pythagorean theorem, we can find the length of the slant edge.

The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Using this, we get:
s^2 + s^2 = slant_edge^2
2s^2 = slant_edge^2
slant_edge = sqrt(2s^2)

Since each side of the square base is equal to 's', we have:
slant_edge = sqrt(2 * s^2)
slant_edge = sqrt(2) * s

5. Calculating the length of the slant edge:
To find the slant edge, we need to calculate the length of each side of the square base.

Since the base area is equal to s^2, we can rearrange the formula to solve for 's':
s = sqrt(base_area)
s = sqrt(46.15)
s ≈ 6.79 cm

Now, we can calculate the length of the slant edge:
slant_edge = sqrt(2) * s
slant_edge = sqrt(2) * 6.79
slant_edge ≈ 9.6 cm

6. Rounding to the nearest integer:
The question asks us to round the length of the slant edge to the nearest integer.

The length of the slant edge, rounded to the nearest integer, is 10 cm.

Therefore, the correct answer is option C) 14 cm.
Free Test
FREE
Start Free Test
Start Free Test
Community Answer
Solve the following question and mark the best possible option.Q.The v...


Thus , required length or slantedge
Attention CAT Students!
To make sure you are not studying endlessly, EduRev has designed CAT study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in CAT.
< Previous Question Next Question >
Explore Courses for CAT exam

Similar CAT Doubts

Directions: Study the following information and answer the question given below.Five students - P, Q, R, S and T were preparing an act for their annual function. They were facing south, but not necessarily in the same order. The distances between two adjacent students are successive multiples of 5 (i.e. the distance between the first and the second student is 5 m, the first and the third student is 10 m, and between the first and the fourth student is 15 m, and so on.)Also,Q is the immediate neighbour of T.There are two students between S and R.P is second to the right of Q.R is not adjacent to P.Student P turned 180° and walked straight for 10 m, and reached point A. Student R walked some distance to reach point A. Student T walked 10$\ \sqrt{2}$ m to reach point B in the southwest direction by turning exactly 45°. Student Q walked some distance straight due south to reach a point which is horizontally in line with point B.Q. What is the distance between student S and point B?

Directions: Read the given information carefully and answer the question that follows.A spy of XYZ kingdom regularly spies between seven enemy camps that are located inside a forest, and are connected to each other by forest roads, FR–1, FR–2, FR–3, FR–4, FR–5, FR–6, and FR–7. The spy has made a map so that he can travel with ease between camps and get the useful information required. However, while travelling between any two enemy camps, the spy always chooses the route which passes through the minimum possible number of enemy camps. If two or more routes pass through the minimum number of enemy camps, he chooses the route for which the distance is also the least. The length of the forest road, directly connecting any two enemy camps, is a multiple of 10. For any pair of enemy camps, the length of a route connecting the two enemy camps and passing through the minimum possible number of enemy camps, is called a forest road stretch between the two enemy camps. The least among all the forest road stretches between two enemy camps is called the minimum forest road stretch between the two enemy camps.The following information is known about the distances between the enemy camps:1. The minimum forest road stretch between FR–4 and FR–6 is 90 miles, while the minimum forest road stretch between FR–2 and FR–6 is 30 miles.2. The highest forest road stretch between FR–1 and FR–7 is 360 miles.3. The minimum forest road stretch between FR–4 and FR–7 is 30 miles.4. The sum of the lengths of the road directly connecting FR–5 to FR–6 and that directly connecting FR–5 and FR–7 is 100 miles.5. The minimum forest road stretch between FR–7 and FR–2 is 70 miles, while the minimum forest road stretch between FR–3 and FR–7 is 110 miles.6. The length of the road directly connecting FR–3 and FR–6 is greater than 110 miles.7. The minimum forest road stretch between FR–1 and FR–4 is 110 miles, while the highest forest road stretch between FR–2 and FR–3 is 240 miles.If the spy has to travel from FR-1 to FR-7, the distance (in miles) that the spy would have to cover is

Directions: Study the following information and answer the question given below.Five students - P, Q, R, S and T were preparing an act for their annual function. They were facing south, but not necessarily in the same order. The distances between two adjacent students are successive multiples of 5 (i.e. the distance between the first and the second student is 5 m, the first and the third student is 10 m, and between the first and the fourth student is 15 m, and so on.)Also,Q is the immediate neighbour of T.There are two students between S and R.P is second to the right of Q.R is not adjacent to P.Student P turned 180° and walked straight for 10 m, and reached point A. Student R walked some distance to reach point A. Student T walked 10$\ \sqrt{2}$ m to reach point B in the southwest direction by turning exactly 45°. Student Q walked some distance straight due south to reach a point which is horizontally in line with point B.Q. In which of the following directions is Q currently positioned with respect to the initial position of R?

Top Courses for CATView all

Top Courses for CAT

Solve the following question and mark the best possible option.Q.The volume of a pyramid with a square base is 200 cm3. The height of the pyramid is 13 cm. What will be the length of the slant edges (i.e. the distance between the apex and any other vertex), rounded to the nearest integer?a)12 cmb)13 cmc)14 cmd)15 cme)16 cmCorrect answer is option 'C'. Can you explain this answer?
Question Description
Solve the following question and mark the best possible option.Q.The volume of a pyramid with a square base is 200 cm3. The height of the pyramid is 13 cm. What will be the length of the slant edges (i.e. the distance between the apex and any other vertex), rounded to the nearest integer?a)12 cmb)13 cmc)14 cmd)15 cme)16 cmCorrect 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 Solve the following question and mark the best possible option.Q.The volume of a pyramid with a square base is 200 cm3. The height of the pyramid is 13 cm. What will be the length of the slant edges (i.e. the distance between the apex and any other vertex), rounded to the nearest integer?a)12 cmb)13 cmc)14 cmd)15 cme)16 cmCorrect 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 Solve the following question and mark the best possible option.Q.The volume of a pyramid with a square base is 200 cm3. The height of the pyramid is 13 cm. What will be the length of the slant edges (i.e. the distance between the apex and any other vertex), rounded to the nearest integer?a)12 cmb)13 cmc)14 cmd)15 cme)16 cmCorrect answer is option 'C'. Can you explain this answer?.
Solutions for Solve the following question and mark the best possible option.Q.The volume of a pyramid with a square base is 200 cm3. The height of the pyramid is 13 cm. What will be the length of the slant edges (i.e. the distance between the apex and any other vertex), rounded to the nearest integer?a)12 cmb)13 cmc)14 cmd)15 cme)16 cmCorrect answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for CAT. Download more important topics, notes, lectures and mock test series for CAT Exam by signing up for free.
Here you can find the meaning of Solve the following question and mark the best possible option.Q.The volume of a pyramid with a square base is 200 cm3. The height of the pyramid is 13 cm. What will be the length of the slant edges (i.e. the distance between the apex and any other vertex), rounded to the nearest integer?a)12 cmb)13 cmc)14 cmd)15 cme)16 cmCorrect answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of Solve the following question and mark the best possible option.Q.The volume of a pyramid with a square base is 200 cm3. The height of the pyramid is 13 cm. What will be the length of the slant edges (i.e. the distance between the apex and any other vertex), rounded to the nearest integer?a)12 cmb)13 cmc)14 cmd)15 cme)16 cmCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for Solve the following question and mark the best possible option.Q.The volume of a pyramid with a square base is 200 cm3. The height of the pyramid is 13 cm. What will be the length of the slant edges (i.e. the distance between the apex and any other vertex), rounded to the nearest integer?a)12 cmb)13 cmc)14 cmd)15 cme)16 cmCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of Solve the following question and mark the best possible option.Q.The volume of a pyramid with a square base is 200 cm3. The height of the pyramid is 13 cm. What will be the length of the slant edges (i.e. the distance between the apex and any other vertex), rounded to the nearest integer?a)12 cmb)13 cmc)14 cmd)15 cme)16 cmCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice Solve the following question and mark the best possible option.Q.The volume of a pyramid with a square base is 200 cm3. The height of the pyramid is 13 cm. What will be the length of the slant edges (i.e. the distance between the apex and any other vertex), rounded to the nearest integer?a)12 cmb)13 cmc)14 cmd)15 cme)16 cmCorrect answer is option 'C'. Can you explain this answer? tests, examples and also practice CAT tests.
Explore Courses for CAT exam

Top Courses for CAT

Explore Courses

Suggested Free Tests

Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev
Get App
© 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