1. 1 Cylinders and Cones

2. 2 Surface Area (SA) = ph + 2B = 2πrh + 2πr 2 Cylinders are right prisms with circular bases. Therefore, the formulas for prisms can be used for cylinders. Volume (V) = Bh = The base area is the area of the circle: The lateral area is the area of the rectangle: 2πrh h 2πr h Formulas: S.A. = 2πrh + 2πr 2 V =

3. 3 For the cylinder shown, find the surface area and volume. 4 cm 3 cm S.A.= 2πrh + 2πr 2 S.A.= 2π(3)(4) + 2π(3) 2 S.A.= 24π + 18π S.A.= 42π sq. cm. V = πr 2 h V = π(3) 2 (4) V = 36π

4. 4 S u r f a c e A r e a ( S A ) = B + L A = π r ( r + l) Cones are right pyramids with a circular base. Therefore, the formulas for pyramids can be used for cones. Volume (V) = The base area is the area of the circle: Notice that the height (h) (altitude), the radius and the slant height create a right triangle. l r h Formulas: S.A. = π r l + πr 2 V =

5. 5 For the cone shown, find the surface area and volume. Note: We must use the Pythagorean theorem to find l. 6 cm 8 10 S.A.= πr (r + l ) S.A.= π6 (6 + 10) S.A.= 6π (16) S.A.= 96π sq. cm. V= 96π cubic cm.