Mensuration
- A solid metallic spherical ball of diameter 6 cm is melted and recasted into a cone with diameter of the base as 12 cm. The height of the cone is
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Radius of ball = 3 cm
Volume of the metallic spherical ball = 4 × π × (3)³ = 36π cm³ 3
Let h be the height of the cone. Volume of cone = Volume of ball⇒ 4 × π × 6 × 6 × h = 36π 3 ⇒ h = 36π × 3 = 3 cm π × 6 × 6 Correct Option: D
Radius of ball = 3 cm
Volume of the metallic spherical ball = 4 × π × (3)³ = 36π cm³ 3
Let h be the height of the cone. Volume of cone = Volume of ball⇒ 4 × π × 6 × 6 × h = 36π 3 ⇒ h = 36π × 3 = 3 cm π × 6 × 6
- The diameter of the iron ball used for the shot-put game is 14 cm. It is melted and then a solid cylinder of height
2 1 cm 3
is made. What will be the diameter of the base of the cylinder ?
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Radius of the iron ball = 14/2 = 7 cm
Volume of the ball = 4 π × (7)³ = 3³ 3
Let the radius of cylinder be r cm.∴ Volume of cylinder = πr² × 7 cm³ 3
Clearly,π r² × 7 = 4 π × (7)³ 3 3 ⇒ r² = 4 × 7 × 7 × 7 × 3 7 × 3
⇒ r = √4 × 7 × 7 = 14 cm
∴ Diameter = 2 × 14 = 28 cmCorrect Option: B
Radius of the iron ball = 14/2 = 7 cm
Volume of the ball = 4 π × (7)³ = 3³ 3
Let the radius of cylinder be r cm.∴ Volume of cylinder = πr² × 7 cm³ 3
Clearly,π r² × 7 = 4 π × (7)³ 3 3 ⇒ r² = 4 × 7 × 7 × 7 × 3 7 × 3
⇒ r = √4 × 7 × 7 = 14 cm
∴ Diameter = 2 × 14 = 28 cm
- The radius of the base and height of a metallic solid cylinder are r cm and 6 cm respectively. It is melted and recast into a solid cone of the same radius of base, The height of the cone is :
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Volume of the cylinder = πr² × h
= πr² × 6
= 6πr² cm²
Let the height of the cone be h cm.∴ Volume of the cone = 1 πr²h 3
According to the question,
Volume of the cone = Volume of the cylinder⇒ 1 πr²h = 6πr² 3
⇒h = 18 cm.Correct Option: C
Volume of the cylinder = πr² × h
= πr² × 6
= 6πr² cm²
Let the height of the cone be h cm.∴ Volume of the cone = 1 πr²h 3
According to the question,
Volume of the cone = Volume of the cylinder⇒ 1 πr²h = 6πr² 3
⇒h = 18 cm.
- A solid metallic cone is melted and recast into a solid cylinder of the same base as that of the cone. If the height of the cylinder is 7cm, the height of the cone was
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Volume of the cone = Volume of the cylinder
⇒ 1 πr²h1 = πr²h2 3
⇒ h1 = 3h2 = 3 × 7 = 21 cm.Correct Option: B
Volume of the cone = Volume of the cylinder
⇒ 1 πr²h1 = πr²h2 3
⇒ h1 = 3h2 = 3 × 7 = 21 cm.
- A solid spherical copper ball, whose diameter is 14 cm, is melted and converted into a wire having diameter equal to 14 cm. The length of the wire is
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Volume of the solid sphere
= 4 πr³ 3 = 4 π × 7 × 7 × 7 cu.cm. 3
If the length of wire (cylindrical) be h cm, thenπR²h = 4 × 7 × 7 × 7 3 ⇒ 7 × 7 × h = 4 × 7 × 7 × 7 3 ⇒ h = 28 cm. 3 Correct Option: D
Volume of the solid sphere
= 4 πr³ 3 = 4 π × 7 × 7 × 7 cu.cm. 3
If the length of wire (cylindrical) be h cm, thenπR²h = 4 × 7 × 7 × 7 3 ⇒ 7 × 7 × h = 4 × 7 × 7 × 7 3 ⇒ h = 28 cm. 3
