$A$ solid metallic sphere of radius $10.5 \, cm$ is melted and recast into a number of smaller cones,each of radius $3.5 \, cm$ and height $3 \, cm$. Find the number of cones so formed.

  • A
    $130$
  • B
    $127$
  • C
    $125$
  • D
    $126$

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$A$ cylinder is closed at both ends by $12 \, cm$ high cones. The radius of the cylinder is $5 \, cm$ and the total height of the article is $41 \, cm$. Find the total surface area of the article. $(\pi = 3.14)$ (in $cm^2$)

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The volume of the largest right circular cone that can be cut out from a cube of edge $4.2 \,cm$ is (in $cm^3$)

$CSA$ of a cylindrical tank with diameter $2.1 \, m$ and height $5 \, m$ is $\ldots \ldots \ldots \ldots \, m^2$.

Which of the following correctly matches the information given in Part $I$ and Part $II$?
Part $I$ Part $II$
$1.$ Volume of a cuboid $a.$ $\frac{1}{3} \pi r^{2} h$
$2.$ Volume of a cone $b.$ $\pi r^{2} h$
$3.$ Volume of a cylinder $c.$ $\frac{4}{3} \pi r^{3}$
$4.$ Volume of a sphere $d.$ $lbh$

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