{"id":7607,"date":"2021-10-28T20:50:27","date_gmt":"2021-10-28T15:20:27","guid":{"rendered":"https:\/\/mathemerize.com\/?p=7607"},"modified":"2022-01-16T17:09:04","modified_gmt":"2022-01-16T11:39:04","slug":"formula-for-surface-area-of-cube","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/formula-for-surface-area-of-cube\/","title":{"rendered":"Formula for Surface Area of Cube – Derivation and Examples"},"content":{"rendered":"

Here you will learn formula for surface area of cube (total surface area and lateral surface area), its derivation and examples.<\/p>\n

Let’s begin –<\/p>\n

What is Cube ?<\/h2>\n

A cube is a cuboid which has all its edges or sides equal i.e length = breadth = height = s (side of cube).<\/p>\n

Formula for Surface Area of Cube<\/h2>\n

(a) Total Surface Area of Cube (T.S.A)<\/strong><\/h4>\n
\n

T.S.A = \\(6s^2\\)<\/p>\n

where s is the side of cube.<\/p>\n<\/blockquote>\n

(b) Lateral Surface Area of Cube (L.S.A)<\/strong><\/h4>\n
\n

L.S.A = \\(4s^2\\)<\/p>\n

where s is the side of cube.<\/p>\n<\/blockquote>\n

Also Read<\/strong> : Formula for Volume of Cube \u2013 Derivation & Examples<\/a><\/p>\n

Derivation :<\/h3>\n

Since a cuboid, whose length, breadth and the height are all equal, is called a <\/span>cube<\/span>. If each edge or side of the cube is s<\/span>, then the total surface area of this cube<\/strong> would be 2(s<\/span> <\/span>\u00d7 s<\/span> <\/span>+ s<\/span> <\/span>\u00d7 s<\/span> <\/span>+ s<\/span> <\/span>\u00d7 s<\/span>), i.e., \\(6s^2\\).<\/span><\/p>\n

Suppose, out of the six faces of a cube, we only find the area of the four faces, leaving the bottom and top faces. In such a case, the area of these four faces is called <\/span>lateral surface area <\/span>of the cube. So, <\/span>lateral surface area of a cube<\/strong> of side s is equal to \\(4s^2\\).<\/span> <\/p>\n

Example<\/span><\/strong> : Hameed has built a cubical water tank with lid for his house, with each outer edge 1.5 m long. He gets the outer surface of tank excluding the base, <\/span>covered with square tiles of side 25 cm. Find how much he would spend for tiles, if the cost of the tiles is Rs <\/span>360 per dozen.<\/span> <\/p>\n

Solution<\/span><\/strong> :  Since Hameed is getting the five outer faces of the tank covered with tiles, he would need to know the surface area of the tank, to decide on the number of tiles required.<\/span><\/p>\n

Edge or side of the cubical tank = 1.5 m = 150 cm (= s<\/span>)<\/span><\/p>\n

So, the surface area of tank = 5 \u00d7 150 \u00d7 150 \\(cm^2\\)<\/span><\/p>\n

Area of each square of tile = side \u00d7 side = 25 \u00d7 25 \\(cm^2\\)<\/span><\/p>\n

So, the number of tiles required = surface area of the tank\/area of each tile<\/span><\/p>\n

=\\(5 \u00d7 150 \u00d7 150\\over 25 \u00d7 25\\) = 180<\/span><\/p>\n

Cost of 1 dozen tiles, i.e., cost of 12 tiles = <\/span>360<\/span><\/p>\n

Therefore, the cost of one tile = <\/span>360\/12 =<\/span> <\/span>30<\/span><\/p>\n

So, the cost of 180 tiles = 180 \u00d7 <\/span>30 = Rs <\/span>5400<\/span><\/p>\n\n\n

\n
Next – Formula for Volume of Cuboid<\/a><\/div>\n<\/div>\n\n\n\n
\n
Previous – Formula for Surface Area of Cuboid<\/a><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

Here you will learn formula for surface area of cube (total surface area and lateral surface area), its derivation and examples. Let’s begin – What is Cube ? A cube is a cuboid which has all its edges or sides equal i.e length = breadth = height = s (side of cube). Formula for Surface …<\/p>\n

Formula for Surface Area of Cube – Derivation and Examples<\/span> Read More »<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-global-header-display":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[63],"tags":[676,678,677],"yoast_head":"\nFormula for Surface Area of Cube - Derivation and Examples<\/title>\n<meta name=\"description\" content=\"In this post you will learn formula for surface area of cube (total surface area and lateral surface area), its derivation and examples.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathemerize.com\/formula-for-surface-area-of-cube\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Formula for Surface Area of Cube - 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