Grade 12 Volume and Surface Area Worksheet

This worksheet covers advanced concepts in calculating volume and surface area of various 3D shapes, including composite figures and optimization problems, suitable for Grade 12 mathematics.

Grade 12 Math GeometryVolume and Surface Area

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Includes

2 Short AnswerMultiple ChoiceFill in the BlanksTrue / FalseMatching

Standards

CCSS.MATH.CONTENT.HSG.GMD.A.1CCSS.MATH.CONTENT.HSG.GMD.A.3CCSS.MATH.CONTENT.HSG.MG.A.1

Topics

VolumeSurface AreaGeometryGrade 12Mathematics

8 sections · Free to use · Printable

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Grade 12 Volume and Surface Area

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Read each question carefully and show all your work. Round answers to two decimal places where necessary.

1. A regular square pyramid has a base side length of 10 cm and a slant height of 13 cm. Calculate its volume.

2. A cylindrical tank has a radius of 5 meters and a height of 12 meters. Calculate its total surface area.

3. A solid is composed of a hemisphere on top of a cylinder. The cylinder has a radius of 3 cm and a height of 7 cm. What is the total volume of the solid?

197.92 cm³

226.19 cm³

254.47 cm³

311.02 cm³

4. A rectangular prism has a volume of 216 cm³. If the length, width, and height are in the ratio 1:2:3, then the surface area of the prism is cm².

5. Doubling the radius of a sphere will quadruple its surface area.

True

False

Match each 3D shape with its correct volume formula.

6. Sphere

a. V = πr²h

7. Cone

b. V = (4/3)πr³

8. Cylinder

c. V = (1/3)πr²h