3D Shapes And Volume
Gbogbo ọrọ náà
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.
Ebumnobi
- 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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Ekele diri gi maka imecha ihe karịrị na 3D Shapes And Volume. Ugbu a na ị na-enyochakwa isi echiche na echiche ndị dị mkpa, ọ bụ oge iji nwalee ihe ị ma. Ngwa a na-enye ụdị ajụjụ ọmụmụ dị iche iche emebere iji kwado nghọta gị wee nyere gị aka ịmata otú ị ghọtara ihe ndị a kụziri.
Ị ga-ahụ ngwakọta nke ụdị ajụjụ dị iche iche, gụnyere ajụjụ chọrọ ịhọrọ otu n’ime ọtụtụ azịza, ajụjụ chọrọ mkpirisi azịza, na ajụjụ ede ede. A na-arụpụta ajụjụ ọ bụla nke ọma iji nwalee akụkụ dị iche iche nke ihe ọmụma gị na nkà nke ịtụgharị uche.
Jiri akụkụ a nke nyocha ka ohere iji kụziere ihe ị matara banyere isiokwu ahụ ma chọpụta ebe ọ bụla ị nwere ike ịchọ ọmụmụ ihe ọzọ. Ekwela ka nsogbu ọ bụla ị na-eche ihu mee ka ị daa mba; kama, lee ha anya dị ka ohere maka ịzụlite onwe gị na imeziwanye.
- 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
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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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Ị chọrọ ime ajụjụ ule ọmarịcha gbasara 3D Shapes And Volume? Budata ngwa Green Bridge CBT iji nweta ajụjụ ule ọmarịcha na nyocha zuru ezu gbasara isiokwu a.
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