3D Shapes And Volume
Bayani Gaba-gaba
Three-dimensional shapes are everywhere: the boxes we pack, the cans on a shelf, the footballs on a pitch. Understanding how to name these solids, count their faces, edges and vertices, and calculate their surface areas and volumes is fundamental to geometry, design, engineering and everyday problem-solving.
This topic covers the properties of common solids (cubes, cuboids, prisms, cylinders, pyramids, cones and spheres), surface area using nets and formulae, volume of prisms using the cross-section method, and metric unit conversions for volume and capacity. Higher tier extends these ideas to the volume and surface area of spheres and cones.
Manufura
- Recognise and give the names of solids
- Understand the terms 'face', 'edge' and 'vertex' in the context of 3D solids
- Find the surface area of simple shapes using the area formulae for triangles and rectangles
- Find the surface area of a cylinder
- Find the volume of prisms, including cuboids and cylinders, using an appropriate formula
- Convert between units of volume within the metric system
- [Higher] Find the surface area and volume of a sphere and a right circular cone using relevant formulae
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- A triangular prism has 5 faces, 9 edges and 6 vertices. Which of the following solids has the same number of faces? A) Cube B) Square-based pyramid C) Tetrahedron D) Hexagonal prism Answer: B
- A cuboid has length 10 cm, width 4 cm and height 3 cm. What is its volume? A) 17 cm cubed B) 120 cm cubed C) 164 cm cubed D) 34 cm cubed Answer: B
- A cylinder has radius 5 cm and height 8 cm. Which expression gives the volume? A) 5 x 5 x 8 B) pi x 5 x 8 C) pi x 25 x 8 D) 2 x pi x 5 x 8 Answer: C
- How many cm cubed are in 1 litre? A) 10 B) 100 C) 1000 D) 10 000 Answer: C
- A sphere has radius 3 cm. Using the formula V = (4/3) x pi x r cubed, what is the volume in terms of pi? A) 12 pi cm cubed B) 36 pi cm cubed C) 108 pi cm cubed D) 27 pi cm cubed Answer: B
Yi aikin wadannan tambayoyi a cikin manhaja
Yi aikin wadannan tambayoyi a cikin manhaja
Littattafan da ake ba da shawarar karantawa
Ƙarin koyo daga tushe na buɗe
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Sashen littafi
Solve Geometry Applications: Volume and Surface Area
Find volume and surface area of rectangular solids
"Prealgebra: Solve Geometry Applications: Volume and Surface Area" by OpenStax, OpenStax, Rice University, licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). Source: https://openstax.org/books/prealgebra/pages/9-6-solve-geometry-applications-volume-and-surface-area. Access for free at https://openstax.org/books/prealgebra/pages/1-introduction
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