Question

A solid metallic cone of height 10 cm, radius of base 20 cm is melted to make spherical balls each of 4 cm. diameter. how many such balls can be made ?

Answer 1

Step-by-step explanation:

Given that

height of cone = 10cm

radius of base of cone = 20cm

diameter of sphere = 4cm

2radius = 4

radius = 2

then according to questions

let the no. of cones = n

$number \: of \: </em><em>sphere</em><em> \: \times volume \: of \: sphere \: = volume \: of \: cone \\ \\ n \times \frac{4}{3} \pi {r}^{3} = \frac{1}{3} \pi {r}^{2}h \\ \\ n \times 4 \times {(2)}^{3} = {(20)}^{2} \times 10 \\ \\ n = \frac{20 \times 20 \times 10}{4 \times 2 \times 2 \times 2} \\ \\ n = 5 \times 5 \times 5 \\ \\ n \: = 125$

therefore the number of spherical ball is 125.

Answer 2

Answer : The Spherical balls can be made from solid metallic is 125

let the spherical balls made = ' x '

According to question,

Formula

Volume of cone = 1/3 πr2h

= (1/3) × π × (20)² ×10

=400 × 10

=(π/3) × 4000

= (4000 / 3 )π

The volume of spherical balls = 4/3πr²

=(4/3) × π × (2)²

= 32/3 π

∴ Spherical balls are formed from the cones.

∴ The total volume of all spherical comes = volume of cones.

∴ No . of spherical balls = volume of cones / volume of 1 spherical ball

=4000 / 3

=32/3

=4000/32

=125

Therefore the number of spherical balls are 125.

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