Surface Area and Volume Worksheet for Prisms and Cylinders

Print 6 drawn prisms and cylinders with a formula box on the sheet and both answers worked in the key.

Surface area and volume

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Formulas

  • Rectangular prism: V = l × w × h
  • Rectangular prism: SA = 2(lw + lh + wh)
  • Triangular prism: V = area of the triangle × length
  • Triangular prism: SA = 2 triangles + 3 rectangles
  • Cylinder: V = πr²h
  • Cylinder: SA = 2πr² + 2πrh

Find the volume and the surface area of each rectangular prism. Not to scale.

  1. 1.12 cm9 cm8 cm

    V = cm³SA = cm²

  2. 2.5 cm7 cm8 cm

    V = cm³SA = cm²

Find the volume and the surface area of each triangular prism. Not to scale.

  1. 3.24 cm10 cm26 cm7 cm

    V = cm³SA = cm²

  2. 4.21 cm20 cm29 cm13 cm

    V = cm³SA = cm²

Find the volume and the surface area of each cylinder. Use 3.14 for π. Not to scale.

  1. 5.8 cm18 cm

    V = cm³SA = cm²

  2. 6.7 cm12 cm

    V = cm³SA = cm²

Sheet D9XR96 · Made at homeroomtools.com

Answer key: Surface area and volume

  1. 1.V = 864 cm³ (12 × 8 × 9); SA = 552 cm² (2 × (96 + 108 + 72))
  2. 2.V = 280 cm³ (5 × 8 × 7); SA = 262 cm² (2 × (40 + 35 + 56))
  3. 3.V = 840 cm³ (½ × 24 × 10 × 7); SA = 660 cm² (240 + (24 + 10 + 26) × 7)
  4. 4.V = 2730 cm³ (½ × 21 × 20 × 13); SA = 1330 cm² (420 + (21 + 20 + 29) × 13)
  5. 5.V = 3617.28 cm³ (3.14 × 8² × 18); SA = 1306.24 cm² (2 × 3.14 × 8 × (8 + 18))
  6. 6.V = 1846.32 cm³ (3.14 × 7² × 12); SA = 835.24 cm² (2 × 3.14 × 7 × (7 + 12))

Sheet D9XR96 · answer key · Made at homeroomtools.com

6 problems on one page, plus the answer key. Sheet D9XR96.

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Volume and surface area formulas

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The key is worked out with whole-number arithmetic from the lengths printed on each drawing, so an answer is exact: a whole number, a decimal that ends, or a multiple of π. With 3.14 for π an answer is rounded to the nearest hundredth only when it has to be, and the key marks it with ≈.

SolidVolumeSurface area
CubeV = s³SA = 6s²
Rectangular prism (cuboid)V = l × w × hSA = 2(lw + lh + wh)
Triangular prismV = area of the triangle × lengthSA = 2 triangles + 3 rectangles
CylinderV = πr²hSA = 2πr² + 2πrh
Square pyramidV = ⅓ × b² × hSA = b² + 2bs, where s is the slant height
ConeV = ⅓πr²hSA = πr² + πrs, where s is the slant height
SphereV = 4/3 × πr³SA = 4πr²

Every sheet has a short code, printed at the foot of the sheet and of its answer key. A share link brings the same sheet back, figure for figure, so a key printed later still fits the copies you handed out.

How it works

This free surface area and volume worksheet has 6 solids on 1 page: rectangular prisms, triangular prisms and cylinders, V and SA on each. Set Find to Volume for a volume of prisms and cylinders worksheet with no surface area.

Read the full guide

Volume only, or surface area only

On the sheet lists 7 solids plus Missing dimension. With Find on Volume, the two prism pills alone make a volume of prisms worksheet: 6 problems on 1 page, and triangular prisms drop the sloping side. Light all 7 for a volume of 3d shapes worksheet: 8 problems on 2 pages.

π, the formula box and pages

Pi swaps Use 3.14 for Leave π in: the first cylinder's key goes from 3617.28 to 1152π cm³. With whole-number lengths no answer is rounded. Formula box on the sheet makes a surface area formula worksheet: V and SA lines for each lit solid. Untick for a quiz. With Find on Both, the opening solids fit 1 page at 4 or 6 problems; 8 or more take 2.

  • About 3 cylinders in 10 show the diameter. The key then starts with r = 7, so a missed halving shows.
  • When surface area is asked, every triangular prism has right-triangle ends and prints the sloping side, so nobody needs Pythagoras.
  • As area and surface area worksheets these print no flat shapes, only a solid's faces: 2 × (96 + 108 + 72).

Questions and answers

What is the formula for the surface area of a cylinder?

SA = 2πr² + 2πrh: two circles plus the curved side, which unrolls into a rectangle as long as the circumference. For a radius of 8 cm and a height of 18 cm the key works it as 2 × 3.14 × 8 × (8 + 18) = 1306.24 cm².

How do you find the surface area of a triangular prism?

Add the 2 triangles to the 3 rectangles. With right-triangle ends of 24, 10 and 26 cm and a length of 7 cm, the triangles total 240 cm² and the rectangles (24 + 10 + 26) × 7 = 420 cm², so SA = 660 cm².

What grade is surface area and volume?

Grades 6 to 8 in Common Core. Standard 6.G.4 finds surface area from nets, which this page does not draw. 7.G.6 covers the volume and surface area of right prisms, and 8.G.9 the volume of cylinders, cones and spheres.

What is the difference between surface area and volume?

Surface area covers the outside of a solid, in square units. Volume is the space inside, in cubic units. As area and volume worksheets, these sheets print solids only, no flat shapes; every blank ends in its unit, cm³ after V, cm² after SA.

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