Q3 of 35 Page 197

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 centimeters. What is the volume of the second?

Let the volume of first pyramid be V1

Let the base edge of first pyramid be a1


Let the height of first pyramid be h1


Let the volume of second pyramid be V2


Let the area of first pyramid be a2


Let the height of first pyramid be h2


We know that,


Volume of a pyramid


Volume of a first pyramid …..(1)


Volume of a second pyramid …(2)


Given:


⇒ a2 = 2a1 …(a)


Given:


⇒ h2 = 3h1 …(b)


Consider, Volume of a second pyramid


(from a and b)



⇒ V2 = 12×V1


⇒ V2 = 12×180 = 2160cm3


More from this chapter

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1

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

 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?

 4

All edges of a square pyramid are 18 centimetres. What is its volume?

 5

The slant height of a square pyramid is 25 centimetres and its surface area is 896 square centimetres. What is its volume?