A drainage tile is a cylindrical shell 21cm long. The inside and outside diameters are 4.5 cm and 5.1 cm, respectively. What is the volume of clay…

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.