{"id":162988,"date":"2024-02-23T16:04:25","date_gmt":"2024-02-23T10:34:25","guid":{"rendered":"https:\/\/www.gkseries.com\/blog\/?p=162988"},"modified":"2024-02-23T16:04:26","modified_gmt":"2024-02-23T10:34:26","slug":"study-the-following-graph-and-answer-the-questions-the-following-bar-graph-shows-the-dimensions-of-cone-cylinder-and-sphere-in-cm","status":"publish","type":"post","link":"https:\/\/www.gkseries.com\/blog\/study-the-following-graph-and-answer-the-questions-the-following-bar-graph-shows-the-dimensions-of-cone-cylinder-and-sphere-in-cm\/","title":{"rendered":"Study the following graph and answer the questions. The following bar graph shows the dimensions of cone, cylinder and sphere in cm"},"content":{"rendered":"\n

Directions: Study the following graph and answer the questions<\/p>\n\n\n\n

The following bar graph shows the dimensions of cone, cylinder and sphere in cm.<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Now 3 more 3D figure cube, prisms and pyramid notes are given Notes:<\/p>\n\n\n\n

1.            The length of the cube is similar with the diameter of the sphere<\/p>\n\n\n\n

2.            The height of prism is similar to the height of a cone.<\/p>\n\n\n\n

3.            The side of the prism is 3\/5th the radius of the cone.<\/p>\n\n\n\n

4.            The height of the pyramid is similar with the radius of the sphere<\/p>\n\n\n\n

5.            The side of the pyramid is similar with 4\/5th of height of the cylinder<\/p>\n\n\n\n

*             All figures are solid<\/p>\n\n\n\n

*             Base of the prism = square<\/p>\n\n\n\n

*             Base of the pyramid is equilateral triangle<\/p>\n\n\n\n

1) Find the ratio of the volume of the cone to pyramid?<\/p>\n\n\n\n

A. 54:53\u221a(3)<\/p>\n\n\n\n

B. 53:55\u221a(3)<\/p>\n\n\n\n

C. 57:54 \u221a(3)<\/p>\n\n\n\n

D. 165:28 \u221a(3)<\/strong><\/p>\n\n\n\n

E. None of these<\/p>\n\n\n\n

Sol:<\/p>\n\n\n\n

The volume of the cone= 1\/3 *22\/7*r2*h<\/p>\n\n\n\n

=1\/3 *22\/7* 102*18 cm3<\/p>\n\n\n\n

The volume of pyramid<\/p>\n\n\n\n

=1\/3* area of base * height<\/p>\n\n\n\n

=1\/3 *\u221a(3)\/4 *162 *15 cm3<\/p>\n\n\n\n

So the ratio will be<\/p>\n\n\n\n

=> 1\/3 *22\/7*100*18:1\/3*\u221a(3)*64*15<\/p>\n\n\n\n

= 165 :28 \u221a(3)<\/p>\n\n\n\n

2) Find the ratio of volume of cylinder to prism.<\/p>\n\n\n\n

A. 12340:567<\/p>\n\n\n\n

B. 14360:576<\/p>\n\n\n\n

C. 14300:687<\/p>\n\n\n\n

D. 14080:567<\/strong><\/p>\n\n\n\n

E. 15400:786<\/p>\n\n\n\n

Sol:<\/p>\n\n\n\n

The volume of the cylinder = 22\/7 *162 *20cm3<\/p>\n\n\n\n

Volume of the prism= area of base * height<\/p>\n\n\n\n

As the area of the prisms is square<\/p>\n\n\n\n

So area of the base= 6*6=36 cm2<\/p>\n\n\n\n

So the volume= 36 *18 cm3<\/p>\n\n\n\n

So the required ratio= 22\/7*16*16*20:36*18<\/p>\n\n\n\n

=14080:567<\/p>\n\n\n\n

3) Find the difference between the total surfacearea of the sphere and cylinder?<\/p>\n\n\n\n

A. 687 cm2<\/p>\n\n\n\n

B. 753 cm2<\/p>\n\n\n\n

C. 782 cm2<\/p>\n\n\n\n

D. 792 cm2<\/strong><\/p>\n\n\n\n

E. 497 cm2<\/p>\n\n\n\n

Sol:<\/p>\n\n\n\n

The total surfacearea of the sphere= 4 *22\/7<\/p>\n\n\n\n

*15*15<\/p>\n\n\n\n

=88*225\/7=2828.57 cm2<\/p>\n\n\n\n

The total area of the cylinder= perimeter of the<\/p>\n\n\n\n

base *height+2* base area<\/p>\n\n\n\n

=2*22\/7*16*20 +2*22\/7 *16*16<\/p>\n\n\n\n

=22\/7(640+512)<\/p>\n\n\n\n

=22\/7(1152)<\/p>\n\n\n\n

=3620.57cm2<\/p>\n\n\n\n

So, the required difference= 3620.57-<\/p>\n\n\n\n

2828.57=792cm2<\/p>\n\n\n\n

4) The total surfacearea of the cone is how much percent more or less than the total surfacearea of the cube?<\/p>\n\n\n\n

A. 99.5% more<\/p>\n\n\n\n

B. 95.4% less<\/p>\n\n\n\n

C. 94.4% less<\/p>\n\n\n\n

D. 97.6% less<\/p>\n\n\n\n

E. 82.19% less<\/strong><\/p>\n\n\n\n

Sol:<\/strong><\/p>\n\n\n\n

The radius of the cone= 10cm, and the height of<\/p>\n\n\n\n

the cone=18cm<\/p>\n\n\n\n

So, the slant height= \u221a(182+102)<\/p>\n\n\n\n

=\u221a(324+100) =\u221a(424)=20.59cm<\/p>\n\n\n\n

So, the totalsurface area of the cone=22\/7<\/p>\n\n\n\n

*10*20.6 +22\/7 *10*10<\/p>\n\n\n\n

=22\/7(206+100)=22\/7 *306=961.71 cm2<\/p>\n\n\n\n

The total surface area of cube= 6* length *<\/p>\n\n\n\n

length<\/p>\n\n\n\n

=5400 cm2<\/p>\n\n\n\n

So the required percentage=(5400-961.71)\/5400<\/p>\n\n\n\n

*100<\/p>\n\n\n\n

=82.19% less<\/p>\n","protected":false},"excerpt":{"rendered":"

Directions: Study the following graph and answer the questions The following bar graph shows the dimensions of cone, cylinder and sphere in cm. Now 3 more 3D figure cube, prisms and pyramid notes are given Notes: 1.            The length of the cube is similar with the diameter of the sphere 2.            The height of prism […]<\/p>\n","protected":false},"author":419,"featured_media":162991,"comment_status":"open","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-4)","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-4)","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-4)","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":[5138],"tags":[5139],"class_list":["post-162988","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-quantitative-aptitude","tag-quantitative-aptitude"],"_links":{"self":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/162988","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/users\/419"}],"replies":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/comments?post=162988"}],"version-history":[{"count":1,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/162988\/revisions"}],"predecessor-version":[{"id":162992,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/162988\/revisions\/162992"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media\/162991"}],"wp:attachment":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media?parent=162988"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/categories?post=162988"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/tags?post=162988"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}