# Volume Volume The volume of a solid is

- Slides: 37

Volume

Volume �The volume of a solid is the amount of space it occupies. �Volume is measured in cubic units. �Ex: cubic feet or ft 3 �Why is it measured in cubic units? �The volume of a prism is the product of the area of the base (B) and the height. �V = areabase x height

Volume of Rectangular Prisms Formula: V = Bh V = lwh • Example: V = Bh V = lwh V = (3)(4)(6) V = (12)(6) V = 72 in 3 6 in 3 in 4 in

Volume of Rectangular Prisms 3 in 10 cm 2 in 5 in V = Bh V = lwh V = (5)(2)(3) V = (10)(3) V = 30 in 3 10 cm V = Bh V = lwh V = (10)(10) V = (100)(10) V = 1000 cm 3

Volume of Triangular Prisms

Volume of Triangular Prisms �Formula: V = Bh V = (½bh)h • Example: V = Bh V = (½bh)h V = ½(2)(5)(7) V = (5)(7) 2 cm 3 V = 35 cm m 7 c

Volume of Triangular Prisms 14 m 14 in. 15 in . 12 in. V = Bh V = ½bhh V = ½(14)(12)(15) V = (7)(12)(15) V = 1260 in 3 6 m 8 m V = Bh V = ½bhh V = ½(8)(6)(14) V = (4)(6) (14) V = 336 m 3

Volume of Cylinders

Volume of Cylinders 3 cm 6 cm V = Bh V = πr 2 h V = π(6)2(3) V = π(36)(3) V ≈ 339. 292 cm 3 10 cm 8 cm V = Bh V = πr 2 h V = π(4)2(10) V = π(16)(10) V = 160π V ≈ 502. 654 cm 3

Volume of Cylinders �Formula: V = Bh • Example: V = Bh V = πr 2 h V = π(3)2(9) V = π(9) V ≈ 254. 469 m 3 6 m V = πr 2 h 9 m

Volume!!!! Calculate the volume of the trapezoidal prism. 6 in 12 in 10 in 20 in A = Bh

Volume!!!! �

More Volume!!! 12 cm 4 cm 6 cm

Volume!!!!! 8 ft 6 ft 12 ft

�Calculate the volume of the pyramid. 10 in 6 in

�Calculate the volume of the pyramid. 12. 5 cm 6 in 6 cm 9 cm

Calculate the volume of the pyramid. 8 ft 2 ft 5 ft

Calculate the volume of the pyramid. 4. 25 mm 2 mm 7 mm

Volume!!!! 15 mm 7 mm 9 mm

Calculate the Volume of the Cylinder 8 in 5 in

Calculate the Volume of the Cone 8 in 5 in

Calculate the Volume of the Cone 11 in 6 in

Calculate the volume of the cone Draw the cone described. Calculate the volume. Diameter: 5 ¾ inches Height: 10 ½ inches 90. 88 cubic inches

Calculate the volume of the pyramid and cone. 8 cm 3 cm 9 in 10 in 4 cm 3 in

Real Life Application Mrs. Pence is enlarging the patio in her back yard. Look at the diagram of the existing patio and calculate how many cubic yards of concrete is needed to make it the proposed size. 3 ft 12 ft 3 ft Patio 20 ft 3 ft HOUSE concrete depth: 6 inches.

Tower of Pisa in Pisa, Italy About 56. 70 m high Diameter of base: About 15. 484 meters The Leaning Tower of Pisa is a bell tower in Pisa Italy. Construction started in 1173 and went on for over 177 years. The tower started to lean shortly after construction started due to poorly laid foundation. The tower leans toward the southwest at a 3. 99 degree angle. Classify Solid: Cylinder Surface Area: S = 2 B + Ch S = 2πr 2 + 2πrh S = 2π(7. 742)2 + 2π(7. 742)(56. 7) S = 2π(59. 94) + 2π(438. 97) S ≈ 376. 42 + 2756. 73 S ≈ 3133. 15 m 2 Volume: V = Bh V = πr 2 h V = π(7. 742)2(56. 7) V = π(59. 94)(56. 7) V ≈ 10671. 6 m 3

Starbuck’s Coffee Shop Albuquerque, New Mexico 40 feet 30 ft Classify Solid: Rectangular Prism Surface Area: S = 2(lw) + 2(lh) + 2(wh) 50 feet S = 2(50)(40) + 2(50)(30) + 2(40)(30) S = 2(2000) + 2(1500) + 2(1200) S = 4000 + 3000 + 2400 S = 9, 400 ft 2 Volume: V = Bh V = lwh V =50(40)(30) V = 2000(30) V = 60, 000 ft. 3

Spheres Sphere: a 3–dimensional figure made of all points equidistant from a center point The earth is a very big sphere.

Spheres �

Spheres Calculate the volume. 5 cm

Spheres Calculate the volume. 8 cm

Spheres Calculate the volume. 12 cm

Volume of Composite Solids Calculate the volume of the composite solid. 10 ft 15 ft 6 ft

Volume of Composite Solids Calculate the volume of the composite solid. 4 ft 9 ft

Volume of Composite Solids Calculate the volume of the composite solid. 7 ft 9 ft 15 ft 25 ft

Volume Application Mrs. Pence is adding to the size of her patio. Use the diagram to calculate the volume of cubic yards of cement needed. Draw a diagram first! 3 ft 15 ft 20 ft

SA & Volume Review � Find the surface area and volume of each of the solids: 1 3 in 6 in 2 3 3 m 2 in 6 cm 3 m 5 m 5 cm 4 m SA SA SA Vol Vol