- Hexagonal Pyramid A has slant height \(30.1\) m, base edge \(3.0\) m, and apothem \(2.6\) m.
Hexagonal Pyramid B has slant height \(7.0\) m, base edge \(8.0\) m, and apothem \(6.9\) m.
Which pyramid has the greater surface area and by how much? Round your answer to \(1\) decimal place.
- What is the surface area of a right pyramid with a rectangular base of \(6\) cm by \(8\) cm and a height of \(5\) cm?
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Paige is throwing a birthday party and wants to make cone shaped party hats. She wants the radius of the hat to be \(15\) cm and the height to be \(36\) cm. How much paper does she need to make \(4\) hats?
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- Christal is making a conical paper popcorn container. She would like the cone to have a height of \(25\) cm and its open edge to have a circumference of \(55\) cm. She is going to trace out a large circle on a piece of paper, cut out the circle as well as cut along the radius to the centre, and then roll up the piece of paper to make the cone.
- What will the radius of the large circle have to be in order to create the container?
- What will be the area of the paper used to make the container?
- Is it possible for the base area of a pyramid to equal its lateral area? Explain why or why not.
- The surface area of a square-based pyramid is \(1804\) cm2 and its base side length is \(22\) cm.
- Calculate its slant height.
- Calculate its vertical height.
- An octagonal-based pyramid has base side lengths of \(20\) cm and slant height of \(80\) cm. What is the surface area of the pyramid?
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Heather enjoys creating stained glass art. Her next project is to make a lampshade based on the frustum of a square-based pyramid. The side length of the base of the pyramid is \(42\) cm, the height of the entire pyramid would be \(28\) cm, and the actual height of the frustum shade is \(24\) cm.
Determine the total area of the glass used for the lampshade.
- A regular tetrahedron is a pyramid that has congruent equilateral triangles as its base and lateral surfaces.
- In order to calculate the surface area of a regular tetrahedron, we don't need as many measurements as we would for other types of regular pyramids. Why is this?
- Two pieces of information: A regular tetrahedron has edge length \(18\) cm and slant height \(15.6\) cm. Calculate its surface area.
- One piece of information: A regular tetrahedron has edge length \(12\) cm. Calculate its slant height and its surface area.