I. Suface Aea and Volume of any Polyhedon A. Suface Aea um of the aea of it face. (Enough pape to wap it) B. Volume the meaue of pace taken up by a olid in thee-dimenional pace. (box of chocolate laye) II. Pim and Cylinde A. Suface Aea Fomula: Suface Aea of a Right Pim o Right Cylinde page 7 Let a ight pim o cylinde have height h, bae of aea B, and let p be the peimete of each bae. Then the uface aea, SA, i given by: SA = B + ph Ovehead (page 7) M1.14 Definition: If the lateal face of a pim ae all ectangle it i a ight pim. Page 641 B. Volume 1. RIGHT Fomula: Volume of a Right Pim o a Right Cylinde page 76 Let a ight pim o ight cylinde have height h and a bae of aea B. Then it volume, V, i given by V = Bh. GENERAL Fomula: Volume of a Geneal Pim o Cylinde page 78 A pim o cylinde of height h and bae aea B ha volume V = Bh. Oblique Fomula: Volume of a Geneal Pim o Cylinde page 78 A pim o cylinde of height h and bae ae B ha volume V = Bh ovehead M1.16 page 77 Page 1
EXAMPLE 1: Find how much pape it would take to wap the biefcae (ignoe the handle)? How many cubic inche of pace doe it povide? inche wide by 1 inche high by 17 inche long. EXAMPLE : A can of oda pop i about 9.5 cm tall and ha a diamete of about 5.5 cm. How much aluminum i needed to make a can of oda pop? III. Pyamid and Cone A. Suface Aea 1. Pyamid Fomula: Suface Aea of Right Regula Pyamid page 77 Let a ight egula pyamid have lant height, and a bae of aea B and peimete p. Then the uface aea, SA, of the pyamid i given by the fomula SA? B? 1 p Example : A pyamid ha a quae bae 10 cm on a ide. The edge that meet at the apex have length 1 cm. Find the lant height of the pyamid, and then calculate the total uface aea (including the bae) of the pyamid. h Page
. Cone Fomula: Suface Aea of a Right Cicula Cone page 75 Let a ight cicula cone have lant height and a bae of adiu. Then the uface aea, SA, of the cone i given by the fomula SA???? EXAMPLE 4: An ice ceam cone ha a diamete of.5 inche and lant height of 6 inche. What i the lateal uface aea of the cone? B. Volume Fomula: Volume of a Pyamid o Cone page 70 The volume, V, of a pyamid o cone of height h, and bae of aea B i given by V? 1 Bh Example 5: A pyamid ha a quae bae 10 cm on a ide. The edge that meet at the apex have length 1 cm. Find the volume of that pyamid. h Page
IV. Sphee 1. Suface Aea Fomula: Suface Aea of a Sphee page 7 The uface aea of a phee of adiu i given by the fomula SA? 4? Example 6: If the diamete of the phee 6 mm find it uface aea. i. Volume Fomula: Volume of a Sphee page 71 The volume, V, of a phee of adiu i given by the fomula 4 V?? EXAMPLE 7: Find the Volume of the above Sphee fom example 6. EXAMPLE 8: An ice ceam cone i 5 inche high (height) and ha an opening inche in diamete. If filled with ice ceam and given a hemipheical (half a phee) top, how much ice ceam i thee? 5 Page 4
V. Similaity Theoem: The Similaity Pinciple of Meauement page 74 Let Figue I and II be imila. Suppoe ome length dimenion of Figue II i k time the coeponding dimenion of Figue I; that i, k i the cale facto. Then: 1. any length meauement peimete, diamete, height, lant height, and o on of Figue II i k time that of the coeponding length meauement of Figue I;. any aea meauement uface aea, aea of a bae, lateal uface aea, and o on of Figue II i k time that of the coeponding aea meauement of Figue I;. any volume meauement total volume, capacity, half-full, and o on- of Figue II i k time the coeponding volume meauement of Figue I. EXAMPLE 9: Televiion et ae meaued by the length of the diagonal of the ectangula ceen. How many time lage i the ceen aea of a 40-inch model than a 1-inch table model? Page 5