Question

A shot-putt is a metallic sphere of radius 8 cm. If the density of the metal is 3 g per cm3, find the mass of the shot-putt.

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Answer 1

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• A shot-putt is a metallic sphere of radius 8 cm. If the density of the metal is 3 g per cm³ , Find the mass of the shot-putt

$\underline{\underline{\sf{\maltese\:\:Given}}}$

• Radius of metallic sphere = 8 cm
• Density = 3 g per cm³

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• The Mass of the shot-putt

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• Mass = 1478.847 g

$\underline{\underline{\sf{\maltese\:\:Calculations}}}$

Density = Mass/Volume

⇒ Density = Mass/Volume of sphere

⇒ Density = Mass/[4/3 πr³]

⇒ Density = Mass/[4/3 × π × r³]

Since π = 22/7

⇒ Density = Mass/[4/3 × 22/7 × r³]

⇒ Density = Mass/[(4 × 22)/(7× 3) × r³]

⇒ Density = Mass/[88/21 × r³]

Given r = 4.9 cm

⇒ Density = Mass/[88/21 × (4.9 cm)³]

⇒ Density = Mass/[88/21 × (4.9 × 4.9 × 4.9) cm³]

⇒ Density = Mass/[88/21 × 117.649 cm³]

⇒ Density = Mass/[4.190 × 117.649 cm³]

⇒ Density = Mass/[492.949 cm³]

⇒ Density = Mass/492.949 cm³

Given Density = 3 g/cm³

⇒ 3 g/cm³ = Mass/492.949 cm³

Multiplying both Sides by 492.949 cm³

⇒ 3 g/cm³ × 492.949 cm³ = Mass/492.949 cm³ × 492.949 cm³

⇒ 3 g × 492.949  = Mass

⇒ 1478.847 g  = Mass

Switch Sides

⇒ Mass = 1478.847 g

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$\underline{\underline{\sf{\maltese\:\:Diagram}}}$

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\qbezier(2.3,0)(2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,-2.121)(0,-2.3)\qbezier(2.3,0)(2.121,-2.121)(-0,-2.3)\put(0,0){\line(1,0){2.3}}\put(0.5,0.3){\bf\large 8\ cm}\end{picture}$

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