1A square based pyramid has vertex G and base WXYZ. O is the centre of the base and M is the midpoint of YZ. What do GO and GM show in the pyramid?
2In the same pyramid, if XY = a cm, what is the length of OM?
3If the vertical height is h, the slant height is l and the side of the base is a, write the mathematical relation between them.
4What do the lengths GZ, GY, GX and GW represent? Are they equal to one another?
5Write the total surface area of a square based pyramid whose side of base is m cm and slant height is n cm.
6What is the lateral surface area of a square based pyramid if the side of its base is p cm and its slant height is q cm?
7Write the volume of a square based pyramid in terms of r and h, if the side of its base is r cm and its vertical height is h cm.
8Find the area of the triangular surfaces of a square based pyramid if its area of base is z square units and its total surface area is y square units.
9Find the volume of a square based pyramid whose area of base is \( 64 \text{ cm}^2 \) and whose height is 15 cm.
10The total surface area of a square based pyramid is \( 285 \text{ cm}^2 \) and the area of its triangular surfaces is \( 192 \text{ cm}^2 \). Find the area of its base.
11In a square based pyramid PABCD with centre O, the vertical height PO is 8 cm and OM is 12 cm, where M is the midpoint of BC. What are the slant height and the length of a lateral edge?
12In a square based pyramid S on the base MNOP, the slant height SA is 13 cm and the base edge NO is 10 cm. What are the vertical height and the length of a lateral edge?
13Find the total surface area and volume of a square based pyramid whose side of base is 12 cm and slant height is 10 cm.
14Find the total surface area and volume of a square based pyramid whose side of base is 10 cm and vertical height is 12 cm.
15Find the total surface area and volume of a square based pyramid whose side of base is 10 cm and slant height is 13 cm.
16Find the total surface area and volume of a square based pyramid whose side of base is 12 cm and vertical height is 8 cm.
17Find the total surface area and volume of a square based pyramid whose side of base is 16 cm and vertical height is 6 cm.
18Find the total surface area and volume of a square based pyramid whose side of base is 16 cm, vertical height is 15 cm and slant height is 17 cm.
19Sophiya has a pot in the shape of a square based pyramid and fills it with water. How much water can it hold if its height is 25 cm and the side of its base is 30 cm?
20The total surface area of a square based pyramid is \( 800 \text{ cm}^2 \) and its side of base is 16 cm. Find the area of its triangular surfaces and its volume.
21The total surface area of an aquarium in the shape of a square based pyramid is 400 square inches and its slant height is 15 inches. Find the volume of the aquarium.
22A group of tourists visiting Egypt reached a pyramid. Their guide said the area of its base is \( 3600 \text{ m}^2 \) and its height is 50 m. From this, a mathematics expert in the group found its total surface area. What value did he obtain?
23A hotel plans a tent in the shape of a square based pyramid for a group of foreign tourists. Each side of its base is 32 m and its height is 50 m. How much cloth is needed to make the tent, and what is the total cost if cloth costs Rs. 500 per square metre?
24A telephone tower of Nepal Telecommunication Corporation (NTC) is built in Asharam's field. Its base is square, its slant height is 50 ft and its vertical height is 40 ft. What area of land does the tower occupy, and if the rent of the field is Rs. 50 per sq. ft each year, what total rent does NTC pay for 20 years?
25A chocolate is shaped like a pyramid with a square base. Its total surface area is \( 1920 \text{ cm}^2 \) and the side of its base is 30 cm. Find its vertical height.
26A box and a pyramid stand on the same square base and have the same height. The box holds \( 900 \text{ cm}^3 \). How much does the pyramid hold, and why?
27Rina finds the volume of a square based pyramid with base side 10 cm and slant height 13 cm as \( \frac{1}{3} \times 100 \times 13 \). What mistake has she made, and what is the correct volume?
28A square based pyramid has a volume of \( 147 \text{ cm}^3 \) and a vertical height of 9 cm. Find the side of its base.