{"id":14357,"date":"2018-04-04T17:06:21","date_gmt":"2018-04-04T11:36:21","guid":{"rendered":"https:\/\/cracku.in\/blog\/?p=14357"},"modified":"2018-04-04T17:12:23","modified_gmt":"2018-04-04T11:42:23","slug":"cat-questions-on-cones-and-frustum","status":"publish","type":"post","link":"https:\/\/cracku.in\/blog\/cat-questions-on-cones-and-frustum\/","title":{"rendered":"CAT Questions on Cones and Frustum"},"content":{"rendered":"

CAT Questions on Cones and Frustum:<\/strong><\/span><\/p>\n

Practice important mensuration questions on Cones and Frustum. Important solved problems on Geometry Cones topic based on previous solved question papers.<\/p>\n

Download CAT App to Access this on your mobile<\/a><\/p>\n

25 Mocks + 30 Sectionals for Rs. 1249<\/a><\/p>\n

Download CAT Quant Questions PDF<\/a><\/p>\n

Take Free Mock Test for CAT 2018<\/a><\/p>\n

Question 1:\u00a0<\/strong>A cylinder and a cone have the same base radius and the same height. The radius of the cylinder is doubled and its height is tripled while the radius of the cone is tripled and its height is doubled. What is the ratio of the new volumes of the cylinder and the cone?<\/p>\n

a) 3:1
\nb) 1:3
\nc) 1:2
\nd) 2:1<\/p>\n

Question 2:\u00a0<\/strong>There is a cone of radius 4 cm and height 6 cm standing on its base. Now a portion of the cone from the top is cut such that we now have a smaller cone of radius 2 cm and the frustum of the bigger cone. What is the ratio of the volume of the smaller cone to the volume of the frustum of the cone?<\/p>\n

a) 1:14
\nb) 1:7
\nc) 3:35
\nd) 2:27<\/p>\n

Question 3:\u00a0<\/strong>A cone of radius 3 cm and height 4 cm is to be painted from the outside (including the base). If the cost of painting per sq. cm is Rs. 14, then what would be the total cost incurred in painting the cone?<\/p>\n

a) Rs. 1056
\nb) Rs. 2112
\nc) Rs. 528
\nd) Rs. 512
\ne) Rs. 1024<\/p>\n

Download CAT 2018 Syllabus PDF<\/a><\/p>\n

Question 4:\u00a0<\/strong>A solid sphere is melted and recast into a right circular cone with a base radius equal to the radius of the sphere. What is the ratio of the height and radius of the cone so formed?<\/p>\n

a) 4:1
\nb) 3:1
\nc) 4:3
\nd) 3:2<\/p>\n

Question 5:\u00a0<\/strong>Find the altitude to the side BC of the triangle ABC if AB = 10, AC = 10 cm and BC = 16 cm.<\/p>\n

a) 6 cm
\nb) 4 cm
\nc) 8 cm
\nd) 5 cm<\/p>\n

Solutions for\u00a0CAT Questions on Cones and Frustum:<\/strong><\/span><\/p>\n

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

1) Answer (D)<\/strong><\/p>\n

Let the initial radius of cylinder and cone be \u2018r\u2019 and height be \u2018h\u2019
\nSo for cylinder, the new radius is 2r and height is 3h
\nThe volume of the cylinder is $ \\pi (2r)^{2}*3h = 12 \\pi r^{2}h$
\nThe new radius of cone is 3r and its new height is 2h
\nSo the required volume is $\\frac{1}{3}\\pi(3r)^{2}*2h = 6 \\pi r^{2}h$
\nHence the required ratio is 2:1<\/p>\n

Factors of a number – Formulas for CAT<\/a><\/p>\n

Formulas on Number system and factorials\u00a0<\/a><\/p>\n

2) Answer (B)<\/strong><\/p>\n

=The volume of a cone with radius \u2018r\u2019 and height \u2018h\u2019 is $\\frac{1}{3}\\times\\pi\\times r^2\\times h$.
\nThe volume of a frustum of a cone with radii \u2018r\u2019 and \u2018R\u2019 and height \u2018h\u2019 is $\\frac{1}{3}\\times\\pi\\times h\\times (R^2+Rr+r^2)$
\nThe cross section of the cone will be as shown in the figure below.<\/p>\n

<\/p>\n

ABC is the cross section of the larger cone and ADE is the cross section of the smaller cone.
\nLet ‘x’ be the height of the smaller cone.
\nIn the figure, triangles AFE and AGC are similar.
\nSo, $\\frac{AF}{AG}=\\frac{EF}{CG}=>\\frac{x}{x+(6-x)}=\\frac{2}{4}=>x=3$ cm
\nNow the volume of the smaller cone is $\\frac{1}{3}\\times\\pi\\times 2^2\\times 3=4\\pi$
\nThe volume of the frustum of the bigger cone is $\\frac{1}{3}\\times\\pi\\times 3\\times (4^2+4\\times2+2^2)=28\\pi$
\nThe ratio of volumes is $4\\pi:28\\pi=1:7$<\/p>\n

3) Answer (A)<\/strong><\/p>\n

$ l=\\sqrt{r^2+h^2}= \\sqrt{3^2+4^2}=5$ cm
\nTotal surface area of the cone
\n= $\\pi r^2+\\pi rl$
\n= $\\pi \\times (9+15)$
\n= $24\\pi$ $cm^2$
\nTotal cost of painting
\n= $24\\times\\frac{22}{7}\\times14$
\n= Rs. 1056<\/p>\n

4) Answer (A)<\/strong><\/p>\n

Let the radius of the sphere be \u2018r\u2019. Now volume of sphere would be equal to the volume of the cone. So
\n$\\frac{4}{3}\\pi r^{3} = \\frac{1}{3}\\pi r^{2}h$
\n=> $\\frac{4}{3}r = \\frac{1}{3}h$
\n=> h\/r = 4
\nHence the required ratio is 4:1<\/p>\n

5) Answer (A)<\/strong><\/p>\n

Since ABC is an isosceles triangle, the altitude from A bisects BC.
\nLet\u2019s say the point of intersection of altitude from A and side BC is D
\n==> BD = 8 cm
\n==>Altitude $AD^2 = 10^2 – 8^2$ = 36$ ==> AD = 6 cm.<\/p>\n

Take a free CAT online mock test<\/a><\/p>\n

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CAT Questions on Cones and Frustum: Practice important mensuration questions on Cones and Frustum. Important solved problems on Geometry Cones topic based on previous solved question papers. Download CAT Quant Questions PDF Take Free Mock Test for CAT 2018 Question 1:\u00a0A cylinder and a cone have the same base radius and the same height. The […]<\/p>\n","protected":false},"author":21,"featured_media":14361,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"om_disable_all_campaigns":false,"_mi_skip_tracking":false,"footnotes":""},"categories":[3,169,125],"tags":[422],"class_list":{"0":"post-14357","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-cat","8":"category-downloads","9":"category-featured","10":"tag-cat-2018"},"better_featured_image":{"id":14361,"alt_text":"CAT Questions on Cones and Frustum","caption":"CAT Questions on Cones and Frustum","description":"CAT Questions on Cones and 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