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Formula -
Lateral Surface Area of Prism = ph where p is the perimeter of the base and h is the height of the prism
1.) Find the total surface area of the prism shown with dimensions
48 x 26 x 60.
2.) A square based pyramid has isosceles triangles as sides. Each triangular face creates a 60 degree angle with the base of the pyramid. If the diagonal of the base is 12\/2 (12 root 2) solve the total surface area of the pyramid.
3.) The solid to the left is a cone attached to a hemisphere at their bases.The diameter of the hemisphere is 40 and the height of the entire figure is 41. Find the total surface area.
I have put some hints for you.......
Why is the radius drawn in as 20"?
Why is the height 21'? Shouldn't it be 20.5"?
Why is the slant height 29"?
CHALLENGE QUESTION!
4.) A wedge of a cheese has been removed from a wheel of cheese (at left) The angle at the center of the cut is 60 degrees. The radius of the wheel is 7" and the height is 9" . Find the total surface area of the remaining cheese wheel shown.
Answers 1. 6480 units 2. 432 units 3. 1380pi
4. 186.66pi +126
4.) A geologist has a model of the Planet Earth with a half-wedge carved out, revealing its inner layers. If the radii are 8 inches and those shown in the model are all perpendicular, then what is the total surface area of the model shown?
5.) Two identical regular hexagonal pyramids are arranges base to base. The area of the regular hexagon inside the solid is 294 \/3. Each lateral edge to each pyramid is 25. Find the total surface area of the solid.
6.)The square based pyramid has isosceles triangles for its faces. Each triangular face creates a 60 degrees angle with the base of the pyramid. If the diagonal of the base if 12 \/2, solve for the total surface area of the pyramid.
7.)All circles shown are congruent and tangent, each with a radius of 2. The centers of each of the outer 6 circles form a regular hexagon, as shown. Find the area of the shaded region
8.) The radius of the circles in the diagram below is 4 units. Find the area of the shaded region.
ANSWERS: 1.) 1728 - 288pi 2.) 3.) 4.). 272pi 5.) 2016
6.).432 sq units 7.) 24\/3 - 4pi. 8.) 48 - 4pi sq. units 9.) 80sq. uits
Answers:
Example 1 - 96 sq in
Example 2 -352 sq cm
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