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For the following questions answer them individually
A sphere is formed by melting three spheres of radii of the 1 cm, 6 cm and 8 cm. The radius of the new sphere will be
The radius of the base of a conical vessel is 10 cm and its height is 48 cm. The vessel is full of water. This water is poured into a cylindrical vessel having base radius 20 cm. The depth of water in the vessel is
The diagonal of a cube measures $$5 \sqrt 3 cm.$$ The surface area of the cube is $$(in cm^2)$$
For equal circles of radius 4 cm touch each other externally. The area of the region bounded by the four circles $$(in cm^2)$$ is
The radii of two solid right circular cylinders are 4 cm and 3 cm respectively and their heights are (h + 1) cm and (2h + 1) cm respectively. If the areas of the whole surface of the two cylinders are equal, then the ratio of their volumes is
If $$x= \frac{\sqrt{3} + 1}{\sqrt{3} - 1}, xy = 1,$$ the value of $$\left(\frac{x - y}{x + y}\right)^2$$ is
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