[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-297606-105":59,"doc-detail-297606-en":131},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":124,"head_meta":126,"extra_data":128,"updated_unix":130},105,"en","rd-sharma-solutions-class-9-maths-chapter-18-ex-181","RD Sharma Solutions - Class 9 Maths - Chapter 18 - Ex 18.1","","RD Sharma Class 9 Maths Chapter 18 Exercise 18.1 contains a set of surface-area based word problems and computations. It covers lateral and total surface areas of cuboids, lateral and total surface areas of cubes, ratios between total and lateral surface areas, and sheet requirements using area of cuboid surfaces. Additional problems address whitewashing and painting cost using room or box surface areas, tile coverage on a cubical tank excluding the base, percent increase in surface area under edge scaling, and determining dimensions from cost differences at different rates.",{"@graph":69,"@context":123},[70,84,106],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/rd-sharma-solutions-class-9-maths-chapter-18-ex-181/297606/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/rd-sharma-solutions-class-9-maths-chapter-18-ex-181/297606.png","ImageObject",300,407,{"name":92,"@type":93},"Grenda","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-01","2026-09-18",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",27,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"How do you find the total and lateral surface areas of a cuboid?","Question",{"text":113,"@type":114},"Total surface area is calculated as 2(lb + bh + hl), and lateral surface area is calculated as 2(l + b)h, using the cuboid’s length, breadth, and height.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"What is the lateral surface area and total surface area of a cube of edge a?",{"text":118,"@type":114},"Lateral surface area is 4a² and total surface area is 6a².",{"name":120,"@type":111,"acceptedAnswer":121},"If the edge of a cube is increased by 50%, by what percentage does its surface area increase?",{"text":122,"@type":114},"The edge becomes 1.5a, so surface area scales by (1.5)² = 2.25. Hence the surface area increases by 125%.","https://schema.org",{"og:url":83,"og:type":125,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":127,"canonical":83},"index,follow",{"doc_id":129,"site_id":62},297606,1789746177,{"code":4,"msg":5,"data":132},{"doc_id":129,"user_id":133,"nickname":92,"user_avatar":134,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":140,"language":141,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":142,"faqs":143,"seo_title":144,"seo_description":67,"update_tm":130,"read_time":145},7971474921005,"https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0","# RD SHARMASolutionsClass 9 MathsChapter 18Ex 18.1\n\nQ1)Find the lateral surface area and total surface area of a cuboid of length 80 cm,breadth 40 cm and height 20cm.  \nSolution:Given that:  \nCuboid length (I)=80cmBreadth (b)=40cmHeight(h)=20cmWe know that,  \nTotal Surface Area=2[lb+bh+hl]=2[(80)(40)+(40)(20)+(20)(80)]=2[3200+800+1600]=2[5600]=11200 cm²  \nLateral Surface Area=2[l+b]h=2[80+40]20=40[120]=4800 cm²  \nQ2)Find the lateral surface area and total surface area of a cube of edge 10 cm.Solution:  \nCube of edge(a)=10 cmWe know that,  \nCube Lateral Surface Area =4 a²=4(10*10)=400 cm²  \nTotal Surface Area=6 a²=6*10²=600 cm²  \nQ3)Find the ratio of the total surface area and lateral surface area of a cube.Solution:  \nTotal Surface Area of the Cube(TSA)=6a²Where,a=edge of the cube  \nAnd,Lateral surface area of the Cube (LSA)=4 a²Where,a =edge of the cube  \nHence,Ratio of TSA and  \nQ4)Mary wants to decorate her Christmas tree.She wants to place the tree on a wooden block covered withcolored paper with a picture of Santa Claus on it.She must know the exact quantity of paper to buy for thispurpose.If the box has length,breadth,and height as 80 cm,40 cm and 20 cm respectively.How many squaresheets of paper of side 40 cm would she require?  \nSolution:  \nGiven that:  \nMary wants to paste a paper on the outer surface of the wooden block.The quantity of the paper required would beequal to the surface area of the box which is of the shape of a cuboid.  \nThe dimensions of the wooden block are:  \nLength (I)=80cm  \nBreadth (b)=40cm  \nHeight(h)=20cm  \nSurface Area of the wooden box=2[lb+bh+hl]  \n=2[(80*40)+(40*20)+(20*80)]=2[5600]=11200 cm²  \nThe Area of each sheet of the paper=40×40 cm²  \n=1600 cm²  \n=7  \nSo,she would require 7 sheets.  \nQ5)The length,breadth,and height of a room are 5m,4 m and 3 m respectively.Find the cost of whitewashing thewalls of the room and the ceiling at the rate of Rs 7.50 m².  \nSolution:  \nTotal Area to be washed =lb+2(I+b)hWhere,length (1)=5mbreadth (b)=4mheight(h)=3m  \nTherefore,the total area to be white washed is =(5*4)+2*(5+4)*3  \n=74m²  \nNow,The cost of white washing 1m²is Rs.7.50  \nTherefore,the cost of white washing 74 m²=(74*7.50)  \n=Rs.555/-  \nQ6)Three equal cubes are placed adjacently in a row.Find the ratio of a total surface area of the new cuboid tothat of the sum of the surface areas of the three cubes.  \nSolution:  \nLength of the new cuboid=3a  \nBreadth of the cuboid =a  \nHeight of the new cuboid=a  \nThe Total surface area of the new cuboid(TSA)=2(1b+bh+hl)  \n(TSA)₁=2(3a*a+a*a+a*3a)(TSA)₁=14a²  \nThe Total Surface area of three cubes  \n(TSA)₂=3*6a²(TSA)₂=18a²  \nT herefore,  \nT herefore,Ratio is 7:9  \nQ7)A 4cm cube is cut into 1 cm cubes.Calculate the total surface area of all the small cubes.Solution:  \nEdge of the cube(a)=4cm  \nVolume of the cube=a³  \n=4³  \n=64cm³  \nEdge of the cube=1cm³  \nTherefore,  \nTherefore,Total Surface area of all the cubes =64*6*1=384cm²  \nQ8)The length of a hall is 18m and the width 12m.The sum of the areas of the floor and the flat roof is equal tothe sum of the areas of the four walls.Find the height of the hall.  \nSolution:  \nLength of the hall=18mWidth of the hall =12mNow given,  \nArea of the floor and the flat roof =sum of the areas of four walls→2*1b=2*1h+2*bh→1b=1h+bh  \nQ9)Hameed has built a cubical water tank with lid for his house,with each other edge 1.5m long.He gets theouter surface of the tank excluding the base,covered with square tiles of side 25cm.Find how much he wouldspend for the tiles if the cost of tiles is Rs 360 per dozen.  \nSolution:  \nGiven that  \nHameed is getting 5 outer faces of the tank covered with tiles,he would need to know the surface area of the tank,to decide on the quantity of tiles required.  \nEdge of the cubical tank(a)=1.5m =150cm  \nSo,surface area of the tank=5*150*150cm²  \n=180  \nCost of 1 dozen tiles,i.e.,cost of 12 tiles =Rs 360  \nSo,the cost of 180 tiles =180*30=Rs.5400  \nQ10)Each edge of a cube is increased by 50%.Find the pe","cbCaicKK9ZdBAXtF","https://ap.wps.com/l/cbCaicKK9ZdBAXtF","pdf",1033479,11,"English","# Q1\n## Lateral and total surface area of a cuboid\n# Q2\n## Lateral and total surface area of a cube\n# Q3\n## Ratio of TSA to LSA for a cube\n# Q4\n## Sheet/tile requirement from cuboid surface area\n# Q5\n## Whitewashing cost for walls and ceiling\n# Q6\n## Surface-area ratio after combining cubes into a cuboid\n# Q7\n## Total surface area after cutting a cube into smaller cubes\n# Q8\n## Height of a hall from equality of areas\n# Q9\n## Tile cost for a cubical tank excluding base\n# Q10\n## Percentage increase in surface area when edge increases\n# Q11\n## Dimensions of a box from cost difference\n# Q12\n## Cost of iron sheet for a closed tank\n# Q13\n## Tarpaulin area for a shelter (top + four sides)\n# Q14\n## Painting cost for inner surface of an open box","[{\"question\":\"How do you find the total and lateral surface areas of a cuboid?\",\"answer\":\"Total surface area is calculated as 2(lb + bh + hl), and lateral surface area is calculated as 2(l + b)h, using the cuboid’s length, breadth, and height.\"},{\"question\":\"What is the lateral surface area and total surface area of a cube of edge a?\",\"answer\":\"Lateral surface area is 4a² and total surface area is 6a².\"},{\"question\":\"If the edge of a cube is increased by 50%, by what percentage does its surface area increase?\",\"answer\":\"The edge becomes 1.5a, so surface area scales by (1.5)² = 2.25. Hence the surface area increases by 125%.\"}]","RD Sharma Solutions - Class 9 Maths - Chapter 18 - Ex 18.1 | PDF",28]