Mensuration
- The total number of spherical bullets, each of diameter 5 decimeter, that can be made by utilizing the maximum of a rectangular block of lead with 11 metre length, 10 metre breadth and 5 metre width is (assume that p > 3)
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Volume of rectangular block = 11 × 10 × 5 = 550 cubic metre
= 550000 cubic dmVolume of a sphere = 4 π × 5 × 5 × 5 cubic dm. 3 2 2 2 ≈ 500 cubic dm 8 ∴ Required answer = 5000 × 8 = 8800 500 Correct Option: A
Volume of rectangular block = 11 × 10 × 5 = 550 cubic metre
= 550000 cubic dmVolume of a sphere = 4 π × 5 × 5 × 5 cubic dm. 3 2 2 2 ≈ 500 cubic dm 8 ∴ Required answer = 5000 × 8 = 8800 500
- A spherical lead ball of radius 10cm is melted and small lead balls of radius 5mm are made. The total number of possible small lead balls is (Take π = 22/7)
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Volume of bigger ball = 4 πr³ 3 = 4 π × 10 × 10 × 10 cu.cm. 3 Volume of smaller ball = 4 π(0.5)³ 3 ∴ Possible number of smaller balls = 4 π × 10 × 10 × 10 = 8000 3 4 π × 0.5 × 0.5 × 0.5 3 Correct Option: A
Volume of bigger ball = 4 πr³ 3 = 4 π × 10 × 10 × 10 cu.cm. 3 Volume of smaller ball = 4 π(0.5)³ 3 ∴ Possible number of smaller balls = 4 π × 10 × 10 × 10 = 8000 3 4 π × 0.5 × 0.5 × 0.5 3
- The diameter of a circular wheel is 7 m. How many revolutions will it make in travelling 22 km?
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Using Rule 7,
Distance covered by the wheel in one revolution = πd= 22 × 7 = 22 metre 7 ∴ Number of revolutions = 22 × 1000 = 1000 22 Correct Option: D
Using Rule 7,
Distance covered by the wheel in one revolution = πd= 22 × 7 = 22 metre 7 ∴ Number of revolutions = 22 × 1000 = 1000 22
- Some solid metallic right circular cones, each with radius of the base 3 cm and height 4 cm, are melted to form a solid sphere of radius 6 cm. The number of right circular cones is
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Volume of a right circular cone = 1 πr²h = 1 π × (3)² × 4 12π cm³ 7 3 Volume of a solid sphere = 4 × π × (6)³ = 288 π cm³ 3
Let the number of cones be n .
∴ n × 12π = 288π⇒ n = 288π = 24 12π Correct Option: B
Volume of a right circular cone = 1 πr²h = 1 π × (3)² × 4 12π cm³ 7 3 Volume of a solid sphere = 4 × π × (6)³ = 288 π cm³ 3
Let the number of cones be n .
∴ n × 12π = 288π⇒ n = 288π = 24 12π
- The height of a conical tank is 60 cm and the diameter of its base is 64cm. The cost of painting it from outside at the rate of ₹ 35 per sq. m. is :
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Area of the curved surface = πrl
where,lrh = √r² + h² = √(32)² + (60)²
= √4624 = 68 cmArea of the curved surface = πrl = 22 × 32 × 68 7 ∴ Total cost of painting = 22 × 32 × 68 1 = ₹ 23.94 approx. 7 10000 Correct Option: D
Area of the curved surface = πrl
where,lrh = √r² + h² = √(32)² + (60)²
= √4624 = 68 cmArea of the curved surface = πrl = 22 × 32 × 68 7 ∴ Total cost of painting = 22 × 32 × 68 1 = ₹ 23.94 approx. 7 10000
