Using a square and four triangles with dimensions as specified in the picture, a pyramid is made. What is the height of this pyramid? What if the square and triangles are like this?

Let us a be the edge and l be the slant height of the square pyramid. Square pyramid is made up of above dimensions. l = 18 , a = 24 From the above, height is given by h = l 2 - a 2 2 ⇒ h = 18 2 - 24 2 2 ⇒ h = 18 2 - 12 2 ⇒ h = 324 - 144 = 180 ∴ h = 6 5 cm . Hence, height of the pyramid is 6 5 cm . Given, Now, l a t e r a l e d g e = 30 , a = 24 . Slant height is l = l a t e r a l e d g e 2 - r a d i u s 2 l = 30 2 - 12 2 = 900 - 144 = 6 21 h = l 2 - a 2 2 ⇒ h = 6 21 2 - 24 2 2 ⇒ h = 766 - 144 ⇒ h = 612 = 6 17 Hence, height of pyramid is 6 17 cm .

A square pyramid is to be made with the triangles shown here as a lateral face. What I would be its height? What if the base edge is 40 centimetres instead of 30 centimetres?

Here, a be the edge and h be the height and e be the slant edge of the square pyramid. Given, From the above: l 2 = e 2 - a 2 2 ⇒ l = 25 2 - 30 2 2 ⇒ l = 25 2 - 15 2 ⇒ l = 625 - 225 ⇒ l = 400 = 20 We know that, l 2 = h 2 + a 2 2 ⇒ h = l 2 - a 2 2 ⇒ h = 20 2 - 15 2 ⇒ h = 400 - 225 ⇒ h = 175 = 13 . 2 So, height of the pyramid is 13 . 2 cm . Now, base edge is 40 centimetres. l 2 = e 2 - a 2 2 ⇒ l = 25 2 - 40 2 2 ⇒ l = 25 2 - 20 2 ⇒ l = 625 - 400 ⇒ l = 225 = 15 We know that, l 2 = h 2 + a 2 2 ⇒ h = l 2 - a 2 2 ⇒ h = 15 2 - 15 2 ⇒ h = 0 So, height of the pyramid is 0 cm .

E M B I B E

Standard 10 Mathematics Part-2>Chapter 2 - Solids>Exercise 1>Q (5)

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10th Kerala Board

IMPORTANT

Earn 100

Can we make a square pyramid with the lateral surface area equal to the base area?

Important Questions on Solids

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10th Kerala Board

IMPORTANT

Standard 10 Mathematics Part-2>Chapter 2 - Solids>Exercise 2>Q (1)

Using a square and four triangles with dimensions as specified in the picture, a pyramid is made.
Question Image

What is the height of this pyramid?
What if the square and triangles are like this?
Question Image

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10th Kerala Board

IMPORTANT

Standard 10 Mathematics Part-2>Chapter 2 - Solids>Exercise 2>Q (2)

A square pyramid of base edge

10

centimetres and height

12

centimetres is to be made of paper. What should be the dimensions of the triangles?

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10th Kerala Board

IMPORTANT

Standard 10 Mathematics Part-2>Chapter 2 - Solids>Exercise 2>Q (3)

Prove that in any square pyramid, the squares of the height, slant height and lateral edge are in arithmetic sequence.

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10th Kerala Board

IMPORTANT

Standard 10 Mathematics Part-2>Chapter 2 - Solids>Exercise 2>Q (4)

A square pyramid is to be made with the triangles shown here as a lateral face. What I would be its height?

Question Image

What if the base edge is $40$ centimetres instead of $30$ centimetres?

EASY

10th Kerala Board

IMPORTANT

Standard 10 Mathematics Part-2>Chapter 2 - Solids>Exercise 3>Q (1)

Can we make a square pyramid with any four equal isosceles triangles?

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10th Kerala Board

IMPORTANT

Standard 10 Mathematics Part-2>Chapter 2 - Solids>Exercise 4>Q (1)

What is the volume of a square pyramid of base edge $10$ centimetres and slant height $15$ centimetres?

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10th Kerala Board

IMPORTANT

Standard 10 Mathematics Part-2>Chapter 2 - Solids>Exercise 4>Q (2)

Two square pyramids have the same volume. The base edge of one is half that of the other. How many times the height of the second pyramid is the height of the first?

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10th Kerala Board

IMPORTANT

Standard 10 Mathematics Part-2>Chapter 2 - Solids>Exercise 4>Q (3)

The base edges of two square pyramids are in the ratio $1 : 2$ and their heights in the ratio $1 : 3$ . The volume of the first is $180$ cubic centimetres. What is the volume of the second in cubic centimetres?

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