VOLUME & SURFACE AREA

Solutions – Volume of Pyramids & Cones

Pyramid and Cone

Volume of Pyramid = 1/3 ABaseh

Volume of a CONE Volume of a Cone = 1/3 π r2h

Exercises:

V =13!r2h

V =13! (9)(5.2)

V =15.6! ft3

V ! 49 ft3height = 62 !32

height = 27h = 5.2

Exercises:

V =13!r2h

V =13! (5.75)2 (15.2)

V =167.52!cm3

V ! 526.27cm3

V =13ABh

V =13(81)(8)

V = 216in3

V =13ABh

V =13(100)(9)

V = 300 ft3

Applications:

1) How much frozen yogurt can you pack inside a cone that is 5in. high with a radius of 1.25 in ?

V =13!r2h

V =13! (1.25)2 (5)

V = 2.6!V = 8.18in3

2) The eight segments from the center of a cube to the eight corners of the cube form the edges of six pyramids. If one edge of the cube is 4 in., what is the volume of each pyramid, to the nearest cubic inch?

V =13ABh

V =13(16)(2)

V =10.67in3

3.  A water storage tank with a roof that is in the shape of a cone has a diameter of 10 ft. The height of the cylindrical part of the tank is 15 ft. The slant height of the roof is 8 ft.

a)  What is the radius of the tank? radius = 5 ft b)  What is the lateral area of the cylindrical

part of the tank?

LAcyl = !r2h

LA = ! (25)(15)LA = 375!LA !1178.1 ft2

3.  A water storage tank with a roof that is in the shape of a cone has a diameter of 10 ft. The height of the cylindrical part of the tank is 15 ft. The slant height of the roof is 8 ft.

c) What is the surface area of the entire tank? SA = LAcone + LAcyl + Abase

SA = !rl +375! +!r2

SA = ! (5)(8)+375! +! (25)SA = 440!SA !1382.3 ft2

4.  A cone-shaped paper cup is 7 cm high with a diameter of 6 cm. If the ivy plant on Julia’s desk needs 240 mL of water, about how many paper cups of water will she use to water it?

(1 mL = 1 cm3)

Vcone =13!r2h

V =13! (9)(7)

V = 21!cm3

V ! 65.97cm3

240 ml / 65.97 = 3.64 She will use 4 paper cups of water.

5.  The Louvre Pyramid in Paris has a square base with sides 112 feet long. If the volume is 296,875 cubic feet, find the height of the pyramid.

V =13ABh

296,875= 13(12, 544)(h)

890, 625=12,544hh = 71 ft

6.  A model of a volcano constructed for a science project is cone-shaped with a diameter of 8 inches. If the volume of the model is about 201 cubic inches, how tall is the model?

V =13!r2h

201= 13! (16)(h)

603=16!hh =12in