1.

A solid cube of edge length 10 cm was placed in a square pyramid of base length 15 cm. If the perpendicular height of the pyramid is 30 cm, what is the ratio of the volume of cube and the remaining volume of the pyramid?1). 1 ∶ 22). 2 ∶ 33). 3 ∶ 44). 4 ∶ 5

Answer»

VOLUME of CUBE = (edge length)3 = (10)3 = 1000 cm3

Now,

⇒ Volume of a square pyramid = (1/3) × AREA of square base × perpendicular HEIGHT = (1/3) × 15 × 15 × 30 = 2250 cm3

When the cube is placed inside the pyramid,

⇒ Remaining volume of pyramid = 2250 – 1000 = 1250 cm3

∴ Required ratio = 1000 ? 1250 = 4 ? 5


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