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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?
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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.
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Thus , required length or slantedge
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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?
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