Math, asked by rohin111bhattacharya, 9 days ago

Somebody please solve this question ​

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Solution

Given :-

• Sum of the radius of two Sphere = 10 cm
• Sum of her Volume = 880 cm³

Find:-

• Product of the radius of the these two sphere .

Explanation

Using Formula

Volume of Sphere = 4/3(πr³)

Let,

• Radius of first Sphere = r
• Radius of Second Sphere = r'

A/C to question,

(Sum of the radius of two Sphere = 10 cm )

==> r + r' = 10 ------------equ(1)

Again,

(Sum of her Volume = 880 cm³)

==> Volume of first Sphere + Volume of second Sphere = 880

==> (4/3)*πr³ + (4/3)*πr'³ = 880

==> (4/3)π * [r³ + r'³] = 880

==> (r³ + r'³) = 880 * 3/5 * 7/22

==> (r³ + r'³) = 40 * 3/5 * 7

==> (r³ + r'³) = 8 * 3 * 7

==> (r³ + r'³) = 168 --------------equ(2)

We know,

(a³+b³) = (a+b)(a²+b²-ab)

So, apply for equ(2)

==> (r+r')(r²+r'²-rr') = 168

Keep Value by equ(1)

==> 10 * (r²+r'²-rr') = 168

==> (r²+r'²-rr') = 168/10------------equ(3)

Squaring both Side of equ(1)

==> (r+r')² = 10²

==> (r²+r'²+2rr') = 100 -----------equ(4)

Subtract equ(3) & equ(4)

==> -rr' - 2rr' = 16.8 - 100

==> -3rr' = - 83.2

==> rr' = -83.2/(-3)

==> rr' = 27.4

Hence

• Sum of radius of two Sphere will be = 27.4 cm

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