[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-297636-105":59,"doc-detail-297636-en":130},{"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":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","similar-shapes-area-and-volume-gcse-1-9","Similar Shapes (Area and Volume) - GCSE 1 - 9","","A GCSE-style mathematics worksheet focused on similar 3D shapes and scaling relationships between surface area and volume. It provides clear exam instructions on how to present working, answer in the given spaces, and treat diagrams as not accurately drawn unless stated. 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Show all your working out, note that diagrams are not accurately drawn unless indicated, and read each question carefully while managing time.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How are answers for similar shapes related?",{"text":117,"@type":113},"Because the solids are mathematically similar, linear dimensions scale by a common factor, surface areas scale with the square of that factor, and volumes scale with the cube of that factor.",{"name":119,"@type":110,"acceptedAnswer":120},"How is Question 3’s frustum volume found?",{"text":121,"@type":113},"The problem describes a frustum B formed by placing a small cone A on top of a frustum. The task asks for the frustum’s volume, expressed in terms of a surd symbol indicated on the sheet.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},297636,1789987499,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":52,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":39,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":143,"read_time":46},3848291630094,"https://eur-avatar.wpscdn.com/davatar_085a072bc5b1113ac321206ff7593b45","Name:    \nGCSE (1 – 9)  \nSimilar Shapes (Area and Volume)  \nInstructions  \n• Use black ink or ball-point pen.  \n• Answer all questions.  \n• Answer the questions in the spaces provided  \n– there may be more space than you need.  \n• Diagrams are NOT accurately drawn, unless otherwise indicated.  \n• You must show all your working out.  \nInformation  \n• The marks for each question are shown in brackets  \n– use this as a guide as to how much time to spend on each question.  \nAdvice  \n• Read each question carefully before you start to answer it.  \n• Keep an eye on the time.  \n• Try to answer every question.  \n• Check your answers if you have time at the end  \n1.  \nDiagram NOT accurately drawn  \nTwo solid shapes, A and B, are mathematically similar.  \nThe base of shape A is a circle with radius 4 cm.  \nThe base of shape B is a circle with radius 8 cm.  \nThe surface area of shape A is 80 cm2 .  \n(a) Work out the surface area of shape B.  \n  cm2 ( 2 )  \nThe volume of shape B is 600 cm3 .  \n(b) Work out the volume of shape A.  \n  cm 3 ( 2 )  \n2.  \nThe two cylinders, A and B, are mathematically similar.  \nThe height of cylinder B is twice the height of cylinder A.  \nThe total surface area of cylinder A is 180 cm2 .  \nCalculate the total surface area of cylinder B.  \n  ( 3 )  \n3.  \nThe diagram represents a large cone of height 6 cm and base diameter 18 cm.  \nThe large cone is made by placing a small cone A of height 2 cm and base diameter 6 cm on top of a frustum B.  \nCalculate the volume of the frustum B.  \nGive your answer in terms of 􀀁 .  \n  ( 4 )  \n4.  \nDiagram NOT accurately drawn  \nCylinder A and cylinder B are mathematically similar.  \nThe length of cylinder A is 4 cm and the length of cylinder B is 6 cm. The volume of cylinder A is 80 cm3.  \nCalculate the volume of cylinder B.  \n  cm 3 ( 3 )  \n5.  \nX and Y are two geometrically similar solid shapes.  \nThe total surface area of shape X is 450 cm2.  \nThe total surface area of shape Y is 800 cm2.  \nThe volume of shape X is 1350 cm 3.  \nCalculate the volume of shape Y.  \n  cm 3 ( 3 )  \n6.  \nTwo cylinders, P and Q, are mathematically similar.  \nThe total surface area of cylinder P is 90􀀁 c2m .  \nThe total surface area of cylinder Q is 810􀀁 c2m .  \nThe length of cylinder P is 4 cm.  \n(a) Work out the length of cylinder Q.  \n  cm ( 3 )  \nThe volume of cylinder P is 100􀀁 3.cm  \n(b) Work out the volume of cylinder Q.  \nGive your answer as a multiple of 􀀁 .  \n  cm 3 ( 2 )  \n7.  \nTwo cones, P and Q, are mathematically similar.  \nThe total surface area of cone P is 24 cm2.  \nThe total surface area of cone Q is 96 cm 2.  \nThe height of cone P is 4 cm.  \n(a) Work out the height of cone Q.  \nThe volume of cone P is 12cm 3  \n(b) Work out the volume of cone Q.  \n................  \n................  \ncm ( 3 )  \ncm 3 ( 2 )","cbCaicS8Xl7yXCAI","https://ap.wps.com/l/cbCaicS8Xl7yXCAI","pdf",168367,"English","# Instructions\n## Exam rules and guidance\n# Question 1\n## Surface area and volume for similar circular solids\n# Question 2\n## Total surface area for similar cylinders\n# Question 3\n## Volume of a frustum from component cones\n# Question 4\n## Volume for similar cylinders\n# Question 5\n## Volume scaling from surface area\n# Question 6\n## Length and volume for similar cylinders with surd units\n# Question 7\n## Height and volume scaling for similar cones","[{\"question\":\"What exam instructions must be followed on the worksheet?\",\"answer\":\"Use black ink or a ball-point pen, answer all questions, and write answers in the spaces provided. Show all your working out, note that diagrams are not accurately drawn unless indicated, and read each question carefully while managing time.\"},{\"question\":\"How are answers for similar shapes related?\",\"answer\":\"Because the solids are mathematically similar, linear dimensions scale by a common factor, surface areas scale with the square of that factor, and volumes scale with the cube of that factor.\"},{\"question\":\"How is Question 3’s frustum volume found?\",\"answer\":\"The problem describes a frustum B formed by placing a small cone A on top of a frustum. The task asks for the frustum’s volume, expressed in terms of a surd symbol indicated on the sheet.\"}]","Similar Shapes (Area and Volume) - GCSE 1 - 9 | PDF",1789746471]