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.
Includes
Standards
Topics
Grade 12 Volume and Surface Area
Name:
Date:
Score:
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
Related Worksheets
Grade 12 Math: Translations Worksheet
This worksheet focuses on understanding and applying translations in coordinate geometry for Grade 12 students.
Annulus Area Worksheet
Grade 12 Math worksheet on calculating the area of an annulus, including problems with different units and composite shapes.
Cavalieri's Principle Worksheet
Grade 12 Math worksheet on Cavalieri's Principle, exploring its application to calculate volumes of various solids.
Grade 12 Math: Triangular Prisms
This worksheet focuses on understanding and calculating properties of triangular prisms, including surface area and volume.
Slicing 3D Figures Worksheet
Explore the cross-sections of various three-dimensional figures with this Grade 12 Geometry worksheet.
Grade 12 Geometry: Parallel Line Proofs
Worksheet focusing on parallel line theorems and proofs, including alternate interior angles, corresponding angles, and consecutive interior angles.
Angle Pairs Worksheet
A Grade 12 math worksheet focusing on identifying and calculating various angle pairs, including complementary, supplementary, vertical, adjacent, corresponding, alternate interior, and alternate exterior angles.
Grade 12 Cartesian Coordinates Worksheet
A Grade 12 math worksheet focusing on advanced Cartesian coordinate concepts, including distance, midpoint, and geometric properties.