grade 7: objective 2.02 solve problems involving volume and surface area of cylinders, prisms, and...

Grade 7: Objective 2.02

Solve problems involving volume and surface area of cylinders, prisms, and composite shapes

FIND THE VOLUME1.

This is easy!! Think….what is the area of the base? How many bases will fill up the prism?

Step 1: Find the area of the base (multiply the height or altitude of the triangle x width÷2) 4 x 3÷2= 6 ft.²

Step 2: Multiply the base (6ft²) x height of the triangular prism6 x 8 = 48ft³

a  =      50 inb  =      33 inc  =      38 in

FIND THE VOLUME2.

This is easy!! Think….what is the area of the base? How many bases will fill up the rectangular prism?

Step 1: Find the area of the base (multiply the length x width of the rectangle) 50in x 38in = 1900in.²

Step 2: Multiply the base (1900in²) X height of the rectangular prism1900 x 33 = 62,700in³

a  =      7.35 kmb  =      14 kmc  =      14 km

FIND THE VOLUME3.

This is easy!! Think….what is the area of the base? How many bases will fill up the triangular prism?

Step 1: Find the area of the base (multiply the altitude (7.35) x width of the triangle) 7.35kmx 14km ÷2 = 51.45km.²

Step 2: Multiply the base (51.45km²) X height of the triangular prism51.45 x 14 = 720.3km³

a  =      5.88 mb  =      6 mc  =      13 m

FIND THE VOLUME4.

a  =      17.8 cmb  =      11 cm

FIND THE VOLUME5.

This is easy too!Step 1: Find the area of the circle (πr²)

Since 17.8 cm is the diameter we need the radius, divide the diameter measure by 2 = 8.9cm.

Step 2: Square the radius = 8.9 x 8.9 = 79.21cm²

Step 3: Multiply 79.21cm² x π (3.14) = 248.72cm² to get the area of the circle.

Step 4: Multiply the area of the base (248.72cm²) x the height. 248.72cm² x 11cm= 2735.92cm3.

a  =      17.8 cmb  =      11 cm

FIND THE SURFACE AREA5.

This is easy, too!Surface area = finding the area of all of the parts and adding them together.

Step 1: Find the area of the circle (πr²)Since 17.8 cm is the diameter we need the radius, divide the diameter measure by 2 = 8.9cm.Step 2: Square the radius = 8.9 x 8.9 = 79.21cm²Step 3: Multiply 79.21 x π (3.14) = 248.72 to get the area of 1 circle. Since we have 2 circles the area of both bases = 2 x 258.72 = approximately 497.44cm².Step 4: Find the area of the rectangular part of the cylinder (base x height = circumference x 11) C=πd.C=3.14 x 17.8 x 11= 614.81cm²Step 5: Add all of the base areas together 497.44 + 614.81 = 1112.25cm²

a  =      51 inb  =      25 inc  =      32 in

FIND THE SURFACE AREA6.

Top & bottoma x c

Front & Backa x b

Short sidesb x c

a  =      28 mmb  =      45 mmc  =      6.7 mmd  =      53 mm

FIND THE SURFACE AREA7.

back

sides

top

bottom

a  =      41 ydb  =      59 yd

FIND THE VOLUME8.

a  =      44.9 ftb  =      49.1 ftc  =      88 ft

FIND THE VOLUME9.

A water tank has been purchased for the farm. It will be used to water cattle. It is an oval shaped metal

container that is 2.6 feet tall. the area of the bottom of the

tank is 14.2 square feet. If the cattle drink one hundred

eighty-eight cubic feet of water a day, how many times per day will the tank have to

be filled?

10.

Mr. Bloop has a cylindrical water tank on his farm. It is eight feet long and 2 feet 9 inches in diameter. Water

flows out a valve in the bottom of the tank at a rate of 3.7 cubic feet per minute. at

that rate, how long will it take to empty the tank

when the tank is full?

11.

a  =      8 ydb  =      13 yd

FIND THE VOLUME12.

a  =      22.8 cmb  =      10.6 cm

FIND THE SURFACE AREA13.

If you have five 6-in by 6-in x 6-in aluminum cubes and superglue them together in a row, what

is the surface area of the resulting shape made by the five cubes?

14.

Captain Howard had his crew paint the

smokestack on his ship the Sea Snail.

The smokestack is shaped like a cylinder

and is 39 feet 8 inches tall. The radius of the

smokestack's base is nine feet. What is the surface area of the smokestack?

15.

a  =      22.8 cmb  =      10.6 cm

FIND THE LATERAL SURFACE AREA16.

FIND THE SURFACE AREA17.