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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?
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The volume of a pyramid with a square base is 200 cm3. The height of ...
Volume = 1/3 × Area of the base (A2) × Height of the pyramid
(H = 13 cm) Thus, 200 = 1/3 × A2 × 13 ⇒ A2 = 600/13
Therefore, side of the square base = A =(√600 / 13)
Say, diagonal of the base = 2B
Then, B2 + B2 = A2 = 600/13
⇒ B2 = 300/13
(Slant edge of pyramid)2 = H2 + B2
Thus, length of the slant edge
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Most Upvoted Answer
The volume of a pyramid with a square base is 200 cm3. The height of ...
Given information:
- Volume of the pyramid = 200 cm^3
- Height of the pyramid = 13 cm

To find:
- Length of the slant edges (distance between the apex and any other vertex)

Formula for the volume of a pyramid:
- Volume = (1/3) * base area * height

1. Calculation of base area:
- Since the base of the pyramid is square, we can find the area by squaring the length of one side.
- Let the length of one side of the square base be 'a'.
- Base area = a^2

2. Calculation of volume:
- Given volume = 200 cm^3
- Volume = (1/3) * base area * height
- Substituting the values, 200 = (1/3) * a^2 * 13
- Simplifying, 200 = (13/3) * a^2
- Multiplying both sides by 3/13, a^2 = (200 * 3) / 13
- a^2 = 600/13

3. Calculation of slant edge length:
- In a pyramid, the slant edge forms a right triangle with the height and one-half the diagonal of the square base.
- Let the slant edge length be 's' and the diagonal of the square base be 'd'.
- We can find the diagonal using the Pythagorean theorem: d^2 = a^2 + a^2
- Simplifying, d = √2 * a

4. Substituting the values:
- Since the diagonal is equal to √2 times the side length, we have d = √2 * a
- Substituting the value of a^2 from step 2, we have d = √2 * √(600/13)
- Simplifying, d = √(2 * 600/13) = √(1200/13) = (√1200) / (√13)

5. Rounding to the nearest integer:
- The value of (√1200) / (√13) is approximately 11.961.
- Rounding this to the nearest integer, we get 12.

Therefore, the length of the slant edges, rounded to the nearest integer, is 12 cm.
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Group QuestionAnswer the following question based on the information given below.Suraj and Girish were going from Mumbai to Khedagoan, which is a rural area. Suraj went on his bicycle whereas Girish went by bus, but the bus dropped Girish midway. As there was no other means to reach his destination, Girish had to walk the rest of the distance. It is known that the speed of the bus was twice the speed at which Suraj travelled and the walking speed of Girish was half of the speed of Suraj. When the first person reached the destination, the distance travelled by Suraj and Girish was in the ratio a : b.While answering the questions:i. Enter only numerical values.ii. Round off your answer to the nearest integer.Answer the following questions based on the given information.Q.After some time, Girish decided to establish a means of transport for Khedagoan and started a bus service for Khedagoan. After one year, Suraj joined the business and the ratio of the yearly investment of Girish and Suraj was cr.b. After six years of Surajs joining, competition increased, and both Girish and Suraj decided not to continue their business. During this period, Ajay, a friend of Suraj and Girish, invested some amount in a scheme having simple interest r for 2 years. The ratio of the amount received by Ajay after two years to the amount invested by Ajay is the same as that of the profits earned by Girish to that earned by Suraj during their partnership. What is the value of r? ( Enter integer rounded off to the next digit)(Note: Assume that the ratio of the profits earned by Girish to that earned by Suraj during their partnership is the same as the ratio of their total investment.) Correct answer is '17'. Can you explain this answer?

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