Geometry and Mensuration: Level 1 Test 7

The largest circle will have a diameter of side = 14 cm.
The radius = 7 cm
The area = Πr² = 22/7 x 7²=154 cm

$ \displaystyle \begin{array}{l}The\text{ }length\text{ }of\text{ }the\text{ }side\text{ }of\text{ }the\text{ }equilateral\text{ }triangle\\formed\text{ }by\text{ }joining\text{ }the\text{ }center\text{ }of\text{ }the\text{ }bases\text{ }of\text{ }the\text{ }cones\text{ }=\text{ }2r\text{ }units.\\The\text{ }radius\text{ }of\text{ }the\text{ }circle\text{ }drawn\text{ }through\text{ }the\text{ }vertices\\\text{ }is\text{ }actually\text{ }the\,\,2/3\text{ }of\text{ }the\text{ }altitude\text{ }of\text{ }the\text{ }triangle\text{ }\\=~\frac{\frac{2}{3}\times \sqrt{3}}{2}2r\,\,=\,\,\frac{2\times 1.7}{3}r>r\\Thus\text{ }correct\text{ }option\text{ }is\text{ }\left( c \right)\end{array}$

$ \displaystyle \begin{array}{l}The\text{ }kerosene\text{ }level\text{ }=\text{ }height\text{ }of\text{ }the\text{ }cylinder\text{ }\left( liquid\text{ }level \right)\\\frac{1}{3}\times \pi \times {{\left( 2 \right)}^{2}}\times 3=\pi \times {{\left( 2 \right)}^{2}}\times h\\\Rightarrow \,\,h=1\,\,cm\end{array}$

The diameter of both the shapes is same and thus we can conclude that for a height of the radius of the sphere the volume of the cone is always less than the sphere.
Thus the sphere will remain outside the cone by more than 50% always.

$ \displaystyle The\text{ }area\,=\frac{24\times 10}{2}=120\,\,c{{m}^{2}}$