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Question
Read the following passage and answer the questions given below.
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A solid cuboidal toy is made of wood. It has five cone-shaped cavities to hold toy carrots. The dimensions of the toy cuboid are – 10 cm × 10 cm × 8 cm. Each cone carved out – Radius = 2.1 cm and Height = 6 cm
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- Find the volume of wood carved out to make five conical cavities.
- Find the volume of the wood in the final product.
Solution
1. Since,
Volume of cone = `1/3 πr^2h`
Here, r = 2.1 cm and h = 6 cm
∴ Volume of 5 conical cavities = `5 xx 1/3 πr^2h`
= `5 xx 1/3 xx 22/7 xx (2.1)^2 xx 6`
= `(5 xx 22 xx 2.1 xx 2.1 xx 6)/(3 xx 7)`
= `2910.6/21`
= 138.6 cm3
2. Volume of the wood in the final product = Volume of cuboidal log of wood – Volume of five conical cavities
= (10 × 10 × 8) – 138.6
= 800 – 138.6 ...[∵ Volume of cuboid = l × b × h]
= 661.4 cm3
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