9.04 Surface area of pyramids and cones
Find the surface area of the following pyramids:
Consider this regular pentagonal pyramid and its net.
How many identical triangular faces does it have?
Find the area of one triangular face.
Find the total surface area of the triangular faces of the pyramid.
Find the total surface area of the triangular faces of the regular hexagonal pyramid shown:
For each of the following square pyramids:
Find the length of the slant height, correct to two decimal places.
Hence, find the surface area of the square pyramid, correct to one decimal place.
Consider the rectangular pyramid with rectangular base of dimensions 6\text{ cm} by 8\text{ cm} and perpendicular height of 6\text{ cm}.
Find the value of x, correct to two decimal places.
Find the value of y, correct to two decimal places.
Find the surface area of the pyramid, correct to one decimal place.
Find the surface area of a square pyramid with base edge 12 \text{ cm} and perpendicular height 8\text{ cm}.
Find the exact surface area of a square pyramid with base edge 10 \text{ m} and perpendicular height 6\text{ m}.
Find the exact surface area of a rectangular pyramid with base edges 10 \text{ cm} and 14 \text{ cm}, and perpendicular height 12\text{ cm}.
Find the surface area of the following cones, correct to two decimal places:
Find the surface area of the following cones, correct to two decimal places:
A cone with a diameter of 8\text{ cm} and a slope length of 12\text{ cm}.
A cone with a diameter of 17\text{ cm} and a slope length of 21\text{ cm}.
A cone with a diameter of 10\text{ cm} and a perpendicular height of 12\text{ cm}.
A cone with a slant height of 25\text{ cm} and a perpendicular height of 24\text{ cm}.
Find the exact surface area of the following cones:
A cone with a diameter of 18\text{ cm} and a slope length of 15\text{ cm}.
A cone with a radius of 8\text{ m} and a height of 14\text{ m}.
The diagram shows a cone of diameter 5 cm and slant height 11 cm sliced in half. Find the surface area of the solid. Round your answer to two decimal places.
A cone has a surface area of 640\text{ cm}^2 and the radius of its base is 5\text{ cm}.
Find the slant height of the cone, correct to two decimal places.
Hence, find the perpendicular height of the cone, correct to one decimal place.
Some very famous right square pyramids are the Egyptian Pyramids.
The following picture shows the Great Pyramid which has a base of 230 \text{ m} and a slant height of 216 \text{ m}:
Find the surface area of the Great Pyramid.
An ice cream cone is made by folding together a sector of pastry, with a small overlap. The dimensions of the cone are shown in the diagram:
Find the external surface area of the cone in square centimetres. Round your answer to one decimal place.
If the overlap adds an extra 5\% to the area, how much pastry is required to produce the cone? Round your answer to the nearest square centimetre.
The roof of a large public building is in the shape of a rectangular pyramid, as shown below:
Calculate the surface area of the roof, excluding the base of the pyramid. Round your answer to the nearest square metre.
Each tile used on the roof has an area of 600\text{ cm}^2. How many tiles are used to cover the roof?
The Louvre pyramid is a large glass and metal pyramid which serves as the entrance to the Louvre museum in Paris. It is a square pyramid with a perpendicular height of 22\text{ m} and a base length of 35 m.
If the surface of the pyramid (excluding the base) is entirely covered in glass, how many square metres of glass make up the structure? Round your answer to the nearest square metre.