{"id":242919,"date":"2025-07-04T10:22:46","date_gmt":"2025-07-04T10:22:46","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=242919"},"modified":"2025-07-04T10:22:47","modified_gmt":"2025-07-04T10:22:47","slug":"a-triangular-pyramid-with-vertices-tuv-and-w-is-removed-from-the-solid-cube-shown","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/04\/a-triangular-pyramid-with-vertices-tuv-and-w-is-removed-from-the-solid-cube-shown\/","title":{"rendered":"A triangular pyramid with vertices\u00a0T,U,V\u00a0and\u00a0W\u00a0is removed from the solid cube shown."},"content":{"rendered":"\n
A triangular pyramid with vertices T,U,V and W is removed from the solid cube shown.<\/pre>\n\n\n\n
\"\"<\/figure>\n\n\n\n
The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n
The correct answer is 15.<\/p>\n\n\n\n
Here is a step-by-step explanation:<\/p>\n\n\n\n
    \n
  1. Initial Shape: The Cube<\/strong>
    A standard cube has 6 faces, 8 vertices, and 12 edges. The edges of the cube shown in the image are:\n
      \n
    • Top face: TW, WV, VU, UT<\/li>\n\n\n\n
    • Bottom face: SP, PQ, QR, RS<\/li>\n\n\n\n
    • Vertical edges: TP, W(S), VR, U(Q) (assuming standard cube construction where T is above P, etc.)
      This gives a total of 12 edges.<\/li>\n<\/ul>\n<\/li>\n\n\n\n
    • The Operation: Removing a Triangular Pyramid<\/strong>
      The problem states that a triangular pyramid is removed from the cube. This is generally understood as slicing off one of the corners of the cube. When a corner is sliced off, the piece that is removed has the shape of a triangular pyramid (also known as a tetrahedron).<\/li>\n\n\n\n
    • Analyzing the Effect on Edges<\/strong>
      Let’s consider what happens when we slice off a corner, for example, the corner at vertex T.\n
        \n
      • The original cube has 12 edges.<\/li>\n\n\n\n
      • When we make a small cut near the corner T, we are creating a new, small triangular face on the cube.<\/li>\n\n\n\n
      • The three original edges that meet at corner T (TP, TW, and TU) are not completely removed. Instead, they are shortened by the cut. So, the original 12 edges still exist in a modified form.<\/li>\n\n\n\n
      • The new cut creates a new triangular face. This new face has\u00a0three new edges<\/strong>\u00a0that were not there before.<\/li>\n<\/ul>\n<\/li>\n\n\n\n
      • Calculating the Final Number of Edges<\/strong>
        To find the total number of edges on the new solid, we add the newly created edges to the original number of edges.\n
          \n
        • Original number of edges: 12<\/li>\n\n\n\n
        • Number of new edges created by the cut: 3<\/li>\n\n\n\n
        • Total number of edges in the remaining solid = 12 + 3 = 15.<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n
          Visualizing the Change:<\/strong><\/p>\n\n\n\n
          Imagine the original cube with its 12 edges. By cutting off a corner, you are essentially replacing one vertex with a new triangular face. This new face brings with it three new edges. The original edges are only truncated, not eliminated. Therefore, the total edge count increases by three.<\/p>\n\n\n\n
          The mention of vertices T, U, V, and W in the problem can be confusing, as they are all on the same face. However, the fundamental geometric operation described is “removing a triangular pyramid,” which in the context of a cube, standardly means cutting off a corner. This operation results in a solid with 15 edges.<\/p>\n\n\n\n
          \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"
          A triangular pyramid with vertices T,U,V and W is removed from the solid cube shown. The Correct Answer and Explanation is: The correct answer is 15. Here is a step-by-step explanation: Visualizing the Change: Imagine the original cube with its 12 edges. By cutting off a corner, you are essentially replacing one vertex with a new triangular face. This […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","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":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-242919","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/242919","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=242919"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/242919\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=242919"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=242919"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=242919"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}