A spherical cannonball 28 cm in diameter is melted and cast into a right circular cone mould, whose base is 35 cm in diameter. Find the height of the cone.
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i. What should be done if the votes cast in favour and against the motion are equal? ii. How many votes can a member cast
i. A chairman of the general meeting (Mr. P) can exercise casting votes in case of a tie in votes. ii. Under the poll method, a member can cast his votes as per...
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A hollow sphere which has internal and external diameter as 16 cm and 14 cm respectively is melted into a cone with a height of 16 cm. Find the diamet
Correct Answer - 13 cm
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Consider a particle of mass \( m \) having linear momentum \( P \) at position \( r \) relative to the origin \( O \). Which of the following equations correctly relates \( r , P , L \) ? a) \( \left[\left(\frac{d L}{d t}\right)+r x\left(\frac{d P}{d t}\right)\right]=0 \) b) \( \left[\left(\frac{d L}{d t}\right)-r x\left(\frac{d P}{d t}\right)\right]=0 \) c) \( \left[\left(\frac{d L}{d t}\right) \times\left(\frac{d r}{d t}\right) \times P\right]=0 \) d) \( \left[\left(\frac{d L}{d t}\right)-\left(\frac{d r}{d t}\right) \times P\right]=0 \)
Correct answer is (b) We know that \(\tau\) = r × F ∵ \(\tau\) \(= \frac{dL}{dt},\) \(F = \frac{dP}{dt}\) \(\left(\frac{dL}{dt}\right) = r \times \left(\frac{dP}{dt}\right)\) \(\left(\frac{dL}{dt}\right) - r \times \left(\frac{dP}{dt}\right) = 0\)
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A solid cylinder and a solid cone have equal base and equal height. If the radius and the height be in the ratio of 4 : 3
Let the radius of both solids be r and their heights be h units, According to condition, \(\frac{r}{h}=\frac{4}{3}\\\therefore h=\frac{3r}{4}\) TSA of cylinder = \(2\pi r(r+h)\) TSA of cone = \(\pi r (r+l)\) On comparing the ratios, \(=\frac {2\pi r...
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The curved surface area of a right circular cone is 12320 cm^2. If the radius of its base is 56cm, then find its height.
CSA (cone) = πrl = 12320 \(\frac{22}{7}\) × 56 × l = 12320 l = 70 cm h = \(\sqrt{70^2-56^2}\) = 42 cm
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The radius of the base and height of a cone are 5 cm and 12 cm then its slant height
Correct option is (C) 13 cm Slant height of cone is \(l=\sqrt{r^2+h^2}\) \(=\sqrt{5^2+12^2}=\sqrt{25+144}\) \(=\sqrt{169}\) = 13 cm
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The radius of the base and height of a cone are 5 cm and 12 cm then its slant height
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A cone whose height and radius are 6 cm and 8 cm respectively. Then its slant height is
Correct option is (B) 10 cm Slant height of cone is \(l=\sqrt{r^2+h^2}\) \(=\sqrt{6^2+8^2}=\sqrt{36+64}\) \(=\sqrt{100}\) = 10 cm
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A cone whose height and radius are 6 cm and 8 cm respectively. Then its slant height is
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The height of a cone is 12 cm. and its radius is 5 cm. then the slant height of cone is in cm.
Correct option is (A) 13 h = 12 cm, r = 5 cm \(l=\sqrt{r^2+h^2}=\sqrt{5^2+12^2}\) \(=\sqrt{25+144}=\sqrt{169}\) = 13 cm
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