A sphere of maximum volume is 'cut out' from a solid hemisphere of radius r. The ratio of the volume of the hemisphere to that of the cut-out sphere…

Match the given areas of various solid objects with their respective formulae: | List I | List II | |---|---| | Area of solid object | Formula | | (A) Lateral surface area of a cylinder | (I) $\pi r\sqrt{r^2 + h^2}$ | | (B) Total surface area of a hemisphere | (II) $4\pi r^2$ | | (C) Lateral surface area of a cone | (III) $2\pi rh$ | | (D) Surface area of a sphere | (IV) $3\pi r^2$ | (Where, r = radius of the solid shape (or base) and h = height of the solid shape.) Choose the correct answer from the options given below:

A solid, metallic right circular cone of radius 7 cm and height 3 cm is melted into three cubes. If the sides of two cubes are 3 cm and 5 cm, then the side of the third cube will be how much?

The area of a rectangle whose length is 5 more than twice its width is 75 square unit. What is the perimeter of the rectangle?

(A). The angles of depression of two ships from the top of a lighthouse are $60^\circ$ and $45^\circ$ towards the east. If the ships are $300$ meter apart, the height of the lighthouse is $150(3+\sqrt{3})$ $$\newline$ (B). If the surface area of a cube is $726 \text{ m}^2$, then its volume shall be $1331 \text{ m}^3$ $$\newline$ (C) If the ratio of diameters of two spheres is $3:5$, then the ratio of their surface area shall be $9:25$ $$\newline$$ Determine as to which of the statements given above are correct :

If area of a square is 44 cm², find the area of the circle formed by the same perimeter.