Grade 7 Objective 2 02 Solve problems involving

Grade 7: Objective 2. 02 Solve problems involving volume and surface area of cylinders, prisms, and composite shapes

1. FIND THE VOLUME

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 (6 ft²) x height of the triangular prism 6 x 8 = 48 ft³

2. FIND THE VOLUME a = b = c = 50 in 33 in 38 in

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) 50 in x 38 in = 1900 in. ² Step 2: Multiply the base (1900 in²) X height of the rectangular prism 1900 x 33 = 62, 700 in³

3. FIND THE VOLUME a = b = c = 7. 35 km 14 km

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. 35 kmx 14 km ÷ 2 = 51. 45 km. ² Step 2: Multiply the base (51. 45 km²) X height of the triangular prism 51. 45 x 14 = 720. 3 km³

4. FIND THE VOLUME a = b = c = 5. 88 m 6 m 13 m

5. FIND THE VOLUME a = b = 17. 8 cm 11 cm

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. 9 cm. Step 2: Square the radius = 8. 9 x 8. 9 = 79. 21 cm² Step 3: Multiply 79. 21 cm² x π (3. 14) = 248. 72 cm² to get the area of the circle. Step 4: Multiply the area of the base (248. 72 cm²) x the height. 248. 72 cm² x 11 cm= 2735. 92 cm 3.

5. FIND THE SURFACE AREA a = b = 17. 8 cm 11 cm

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. 9 cm. Step 2: Square the radius = 8. 9 x 8. 9 = 79. 21 cm² Step 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. 44 cm². 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. 81 cm² Step 5: Add all of the base areas together 497. 44 + 614. 81 = 1112. 25 cm²

6. FIND THE SURFACE AREA Front & Back axb Top & bottom axc Short sides bxc a = b = c = 51 in 25 in 32 in

7. FIND THE SURFACE AREA back sides bottom top a = b = c = d = 28 mm 45 mm 6. 7 mm 53 mm

8. FIND THE VOLUME a = b = 41 yd 59 yd

9. FIND THE VOLUME a = b = c = 44. 9 ft 49. 1 ft 88 ft

10. 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?

11. 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?

12. FIND THE VOLUME a = b = 8 yd 13 yd

13. FIND THE SURFACE AREA a = b = 22. 8 cm 10. 6 cm

14. 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?

15. 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?

16. FIND THE LATERAL SURFACE AREA a = b = 22. 8 cm 10. 6 cm

17. FIND THE SURFACE AREA