{"id":34338,"date":"2022-05-30T18:25:58","date_gmt":"2022-05-30T12:55:58","guid":{"rendered":"https:\/\/cracku.in\/blog\/?p=34338"},"modified":"2022-08-04T09:16:00","modified_gmt":"2022-08-04T03:46:00","slug":"sphere-questions-for-cat-pdf","status":"publish","type":"post","link":"https:\/\/cracku.in\/blog\/sphere-questions-for-cat-pdf\/","title":{"rendered":"Sphere Questions for CAT PDF"},"content":{"rendered":"

Sphere Questions for CAT PDF<\/span><\/h2>\n

Download important CAT Sphere Questions with Solutions PDF based on previously asked questions in CAT exam. Practice Sphere Questions with Solutions for CAT exam.<\/p>\n

Download Sphere Questions for CAT PDF<\/a><\/p>\n

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

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

Question 1:\u00a0<\/b>It takes 2 liters to paint the surface of a solid sphere. If this solid sphere is sliced into 4 identical pieces, how many liters will be required to paint all the surfaces of these 4 pieces.<\/p>\n

a)\u00a02.2 liters<\/p>\n

b)\u00a02.5 liters<\/p>\n

c)\u00a03.0 liters<\/p>\n

d)\u00a04.0 liters<\/p>\n

e)\u00a0None of the above<\/p>\n

Question 2:\u00a0<\/b>If a right circular cylinder of height 14 $cm$ is inscribed in a sphere of radius 8 \u00a0$cm$, then the volume of the cylinder is:<\/p>\n

a)\u00a0110 $cm^3$<\/p>\n

b)\u00a0220\u00a0$cm^3$<\/p>\n

c)\u00a0440\u00a0$cm^3$<\/p>\n

d)\u00a0660\u00a0$cm^3$<\/p>\n

Question 3:\u00a0<\/b>A cylinder, a Hemi-sphere and a cone stand on the same base and have the same heights. The ratio of the areas of their curved surface is:<\/p>\n

a)\u00a0$2:2:1$<\/p>\n

b)\u00a0$2:\\sqrt{2}:1$<\/p>\n

c)\u00a0$\\sqrt{2}:3:1$<\/p>\n

d)\u00a0None of the above<\/p>\n

Question 4:\u00a0<\/b>Consider the volumes of the following objects and arrange them in decreasing order:
\ni. A parallelepiped of length 5 cm, breadth 3 cm and height 4 cm
\nii. A cube of each side 4 cm.
\niii. A cylinder of radius 3 cm and length 3 cm
\niv. A sphere of radius 3 cm<\/p>\n

a)\u00a0iv,iii,ii,i<\/p>\n

b)\u00a0iv,ii,iii,i<\/p>\n

c)\u00a0iv,iii,i,ii<\/p>\n

d)\u00a0None of the above<\/p>\n

Question 5:\u00a0<\/b>A spherical metal of radius 10 cm is molten and made into 1000 smaller spheres of equal sizes. In this process the surface area of the metal is increased by:<\/p>\n

a)\u00a01000 times<\/p>\n

b)\u00a0100 times<\/p>\n

c)\u00a010 times<\/p>\n

d)\u00a0No change<\/p>\n

e)\u00a0None of the above<\/p>\n

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

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Answers & Solutions:<\/strong><\/span><\/p>\n

1)\u00a0Answer\u00a0(D)<\/strong><\/p>\n

2 litres are required to paint the surface of a solid sphere.
\nSurface area of the solid sphere = $4\\pi*r^2$
\nNow, the solid sphere is cut into 4 identical parts. This is possible only when the sphere is cut into 4 quarter spheres.
\nAfter making the first cut, 2 hemispheres will be formed. 2 circles of area $\\pi*r^2$ will get exposed in addition to the surface area of the sphere (the base surface of the bottom hemisphere and the base of the top hemisphere).
\nNow, another perpendicular cut will be made along the diameter of the sphere. 2 additional surfaces will get exposed again (one on left hemisphere and the another on the right hemisphere).<\/p>\n

Area exposed after making 4 identical pieces = $4*\\pi*r^2$ +\u00a0$2*\\pi*r^2$ +\u00a0$2*\\pi*r^2$
\n=\u00a0$8*\\pi*r^2$
\n2 litres of paint is required to paint an area of $4\\pi*r^2$
\n=> 4 litres of paint will be required to paint an area of\u00a0$8*\\pi*r^2$.<\/p>\n

Therefore, option\u00a0D is the right answer.<\/p>\n

2)\u00a0Answer\u00a0(D)<\/strong><\/p>\n

\"8\"<\/figure>\n

The radius of sphere is 8 $cm$. Then applying Pythagoras, the radius of base of cylinder is $\\sqrt{15}$\u00a0\u00a0$cm$<\/p>\n

The height of cylinder is given as 14 $cm$. Volume of cylinder is $\\pi$ $r^{2}$h<\/p>\n

$\\frac{22}{7}$* 15*14 = 660\u00a0$cm^3$<\/p>\n

3)\u00a0Answer\u00a0(D)<\/strong><\/p>\n

The cylinder, hemisphere and cone stand on the same base and have the same height. Let the radius of the three solids be $r$ and the height be $h$.<\/p>\n

Height of the hemisphere, $h$ = $r$ (Radius)<\/p>\n

Curved surface area of the cylinder = $2*\\pi*r*r$ = $2*\\pi*r^2$
\nCurved surface area of the hemisphere = $2*\\pi*r^2$
\nCurved surface area of the cone = $\\pi*r*\\sqrt{r^2+r^2}$ = $\\pi*r*\\sqrt{r^2+r^2}$ = $\\pi*r^2*\\sqrt{2}$
\nRatio = $2:2:\\sqrt{2}$ = $\\sqrt{2}:\\sqrt{2}:1$
\nAs the answer is not among the given options, option D is the right answer.<\/p>\n

4)\u00a0Answer\u00a0(A)<\/strong><\/p>\n

i. Volume of the parallelepiped of length 5 cm, breadth 3 cm and height 4 cm = 3*4*5 = 60 cm$^3$
\nii. Volume\u00a0 of\u00a0the\u00a0cube of each side 4 cm = 4^3 = 64\u00a0cm$^3$
\niii.Volume\u00a0 of\u00a0the cylinder of radius 3 cm and length 3 cm = $\\pi*3^2*3$ = 84.82 cm$^3$
\niv. Volume\u00a0\u00a0of\u00a0the\u00a0 sphere of radius 3 cm = $4\/3*\\pi*3^3$ = 113.09\u00a0cm$^3$<\/p>\n

Therefore, we can say that\u00a0volumes of the objects in decreasing order =\u00a0iv,iii,ii,i.<\/p>\n

Hence, option A is the correct answer.<\/p>\n

5)\u00a0Answer\u00a0(E)<\/strong><\/p>\n

Radius of larger sphere = $R = 10$ cm<\/p>\n

Let radius of each of the smaller spheres = $r$ cm<\/p>\n

=> $\\frac{4}{3} \\pi R^3 = 1000 \\times \\frac{4}{3} \\pi r^3$<\/p>\n

=> $10^3 = 1000 r^3$<\/p>\n

=> $r = \\sqrt[3]{1} = 1$ cm<\/p>\n

Initial surface area of sphere = $4 \\pi R^2 = 4 \\pi \\times 100 = 400 \\pi$<\/p>\n

Final surface area of 1000 spheres = $1000 \\times 4 \\pi r^2 = 1000 \\times 4 \\pi = 4000 \\pi$<\/p>\n

$\\therefore$ Increase in surface area = $4000 \\pi – 400 \\pi = 3600 \\pi$<\/p>\n

=> $\\frac{3600 \\pi}{400 \\pi} = 9$ times<\/p>\n

Download CAT Previous Papers PDF<\/a><\/p>\n

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We hope this CAT Sphere Questions with Solutions PDF for CAT will be helpful to you.<\/p>\n","protected":false},"excerpt":{"rendered":"

Sphere Questions for CAT PDF Download important CAT Sphere Questions with Solutions PDF based on previously asked questions in CAT exam. Practice Sphere Questions with Solutions for CAT exam. Download CAT Quant Questions PDF Take a free mock test for CAT Question 1:\u00a0It takes 2 liters to paint the surface of a solid sphere. If […]<\/p>\n","protected":false},"author":42,"featured_media":34341,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"om_disable_all_campaigns":false,"_mi_skip_tracking":false,"footnotes":""},"categories":[3,169,125,350],"tags":[6,5119,351,2581,2579],"class_list":{"0":"post-34338","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":"category-iift","11":"tag-cat","12":"tag-cat-2022","13":"tag-iift","14":"tag-important-questions-for-cat","15":"tag-sphere-questions-for-cat"},"better_featured_image":{"id":34341,"alt_text":"Sphere Questions for CAT PDF","caption":"Sphere Questions for CAT PDF\n","description":"Sphere Questions for CAT 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