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Geometry Practice: Area and Surface Area Calculations

A collection of geometry practice problems on finding the area of a circle, faces of a cube, net of a rectangular prism, and surface area of various 3-dimensional objects. Suitable for students and learners of all levels.

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Geometry Practice: Area and Surface Area Calculations

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  1. Do Now 1) Find the area of a circle with a diameter of 10ft. Leave your answer in terms of π. [A= πr2] 2) Round to the nearest whole number. 3) How many faces are on a cube? What shape are the faces?

  2. Net- a 2-dimensional pattern that forms a solid when it is folded. width length width height length height Rectangular Prism 2 ( ) Area of the orange face: ______________________ width x length Net of a Rectangular Prism 2 ( ) Area of the blue face: ______________________ length x height Area of the green face: ______________________ 2 ( ) width x height Surface Area-the sum of the areas of its faces Surface Area of a Rectangular Prism- + 2lh 2wl +2wh

  3. Find the surface area of the rectangular prism. 3 in. height 4 in. width 5 in. length 2(4)(5) +2(4)(3) +2(5)(3) 40 + 24 + 30 in2 94 Surface Area of a Rectangular Prism- + 2lh 2wl +2wh

  4. Find the surface area of the rectangular prism. 6 ft. 13 ft. l w 4 ft. h 2(6)(13) +2(6)(4) +2(13)(4) 156 + 48 + 104 ft2 308 Surface Area of a Rectangular Prism- + 2lh 2wl +2wh

  5. Find the surface area of the rectangular prism. 30 yd. 2ft. 7 cm. h h 6 cm. 9 yd. 2 ft. h 15 ft. w w 20 cm. 12 yd. l l w l = = = 2(6)(20) +2(6)(7) 2(9)(12) +2(9)(30) +2(20)(7) 2(2)(15) +2(2)(2) +2(12)(30) +2(15)(2) + 2wh + 2wh + 2wh 2wl 2wl 2wl + 2lh + 2lh + 2lh 240 + 84 216 + 540 + 280 60 + 8 + 720 + 60 cm2 cm2 601 ft2 1,476 128

  6. Rashid needs to buy some wood to build a box. He must calculate the surface area of the box to determine how much wood to buy. A diagram of the box is shown below. (2006) 2ft. 3ft. 3 ft. How much wood does Rashid need to buy to build the box?

  7. What is the best estimation, in square centimeters, for the surface area of the rectangular prism shown below? (2008) A) 14 B) 20 C) 32 D) 48 5.4 cm 1.9 cm 1.9 cm

  8. Right Triangular Prism Surface area of a Right Triangular Prism = wh + lw + lp + ls 4cm 2cm 5cm = 3(2) +7(3) +7(4) +7(5) 7cm = 6 + 21 + 28 + 35 3cm = 90 cm2

  9. Right Triangular Prism Surface area of a Right Triangular Prism = wh + lw + lp + ls 6ft 3ft 8ft = 4(3) +10(4) +10(6) +10(8) 10ft = 12 + 40 + 60 + 80 4ft = 192 ft2

  10. Practice- Find the surface are of each right triangular prism. 1. 2. 8mm 4yd 7mm 5yd 6mm 4yd yd 9mm 5 mm 4yd

  11. Find the surface area of each 3-dimensional object. 1. 2. 8cm 2mm. h w 5cm 3mm. 12cm l 4mm. 10cm Rectangular Prism 15cm

  12. C = 2πr Area = πr2 Area = πr2 2πr height height Area = πr2 Area = πr2 Cylinder Net of a Cylinder Surface Area of a Cylinder Area of 2 circles + Area of the rectangle 2πr h =2 + πr2

  13. Practice- Find the surface area of the cylinder. Round your answer to the nearest tenth. 1) 2πr h 2 πr2 3 in + SA = 7 in

  14. Practice- Find the surface area of the cylinder. Round your answer to the nearest tenth. 2) 14 mm 5 ft 2πr h 2 πr2 + SA = 3) 9 mm 11 ft

  15. 4) Chris must paint the cylindrical tank shown below. (2007) h = 5 ft 2πr h 2 πr2 + SA = r = 2ft A) What is the surface area of the entire tank to the nearest square foot? B) One can of paint will cover 25 square feet. How many cans of paint must Chris purchase to paint the entire surface area of the tank?

  16. 5) Joel draws a picture of his cylinder shown below. (2006) 7 cm 2πr h 2 πr2 + SA = 15 cm Calculate the volume of Joel's cylinder. Round your answer to the nearest tenth.

  17. Practice - Find the surface area of each 3-dimensional object. 2. 1. 7cm 3. 2 ft 3cm 7cm 8cm 2 cm. 6ft 5cm. Triangular Prism 15cm 4cm. Cylinder Rectangular Prism

  18. Practice - Find the surface area of each 3-dimensional object. 5. 4. 3cm 6. 4 ft 6cm 9cm 2cm 8 cm. 5ft 5cm. 1cm Triangular Cylinder 11cm. Cylinder Rectangular Prism

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