Mensuration Difficult

A birthday hat is in the shape of a cone and has a slant height ‘l’ and the radius of the base (which is a circle) is ‘r’. The curved surface of the hat is a triangle which has base = r and height = l. Form an expression for the total surface area of the hat (i.e. curved surface area + base area).

A table is in the shape of a triangle and its edges are of the lengths 40 cm, 50 cm and 55 cm. Priya wants to find its area in order to find out how many cups it can accommodate for her party. Help her find the area of the table.

A flat bowl (shaped like a cylinder) with height 7 cm and radius 8 cm is filled with water up till 3 cm and placed on a table. A glass (shaped like a cylinder) full of water of height 9 cm and radius 3 cm is put inside the bowl. What is the increase in the water level of the bowl of water after the glass is placed in it?

You have a 3-liter and a 5-liter water container, and neither one is marked aside from the total volume. A tap is also now flowing. In order to measure out exactly 4 liters of water, we must utilize the containers and the tap in the right way. How is this possible?

A hut is a combination of 2 different 3-D shapes which are a cube and a square-based pyramid (all edges of equal length). The breadth of the hut is 5m and there are 3 rectangular windows with length and height 0.5m and 0.75m respectively and a door of height and length 2m and 0.85m respectively. If the hut is constructed using hay, then what is the area of the hut that needs to be covered with hay assuming that the windows and door are empty?