Download Mensuration Questions for CAT<\/a><\/p>\n Enroll for CAT 2022 Crash Course<\/a><\/p>\n Instructions<\/b><\/p>\n Read the following information and answer the questions based on it. Question 1:\u00a0<\/b>How many cuboids shall have all the three colours?<\/p>\n a)\u00a08<\/p>\n b)\u00a010<\/p>\n c)\u00a012<\/p>\n d)\u00a014<\/p>\n e)\u00a0None of these<\/p>\n 1)\u00a0Answer\u00a0(A)<\/strong><\/p>\n Solution:<\/b><\/p>\n The number of cuboid which will have all the three colours are the corner pieces.<\/p>\n Thus, 8 cuboids will have all the three colours.<\/p>\n => Ans – (A)<\/p>\n Question 2:\u00a0<\/b>How many cuboids shall not any colour?<\/p>\n a)\u00a0No any<\/p>\n b)\u00a02<\/p>\n c)\u00a04<\/p>\n d)\u00a06<\/p>\n e)\u00a0None of these<\/p>\n 2)\u00a0Answer\u00a0(D)<\/strong><\/p>\n Solution:<\/b><\/p>\n Number of cuboids which do not have any colour = $(5-2) \\times (4-2) \\times (3-2)$<\/p>\n = $3 \\times 2 \\times 1=6$<\/p>\n => Ans – (D)<\/p>\n Question 3:\u00a0<\/b>How many cuboids shall have only two colours red and green in their two sides?<\/p>\n a)\u00a08<\/p>\n b)\u00a012<\/p>\n c)\u00a016<\/p>\n d)\u00a020<\/p>\n e)\u00a0None of these<\/p>\n 3)\u00a0Answer\u00a0(B)<\/strong><\/p>\n Solution:<\/b><\/p>\n Number of cuboids which\u00a0have only two colours red and green in their two sides are the middle cuboids at the corner edges. There are 4 such edges which have combination of red and green colour.<\/p>\n Number of required cuboids = $(5-2) \\times 4$<\/p>\n = $3 \\times 4=12$<\/p>\n => Ans – (B)<\/p>\n Question 4:\u00a0<\/b>How many cuboids shall have only one colour ?<\/p>\n a)\u00a012<\/p>\n b)\u00a016<\/p>\n c)\u00a022<\/p>\n d)\u00a028<\/p>\n e)\u00a0None of these<\/p>\n 4)\u00a0Answer\u00a0(E)<\/strong><\/p>\n Solution:<\/b><\/p>\n Number of cuboids which have only 1 colour are the middle cuboids in all the faces. Also, there are 2 types of each faces.<\/p>\n 2*(B-2)*(H-2)+2*(H-2)*(L-2).<\/p>\n =2*(4-2)*(3-2)+2*(3-2)*(5-2)+2*(5-2)*(4-2).<\/p>\n = 2*2*1 + 2*1*3 + 2*3*2.= 4 + 6 + 12.<\/p>\n =22.<\/p>\n Question 5:\u00a0<\/b>The sum of the radius and height of a cylinder is 42 cm. Its total surface area is 3696 cm 2. What is the volume of cylinder ?<\/p>\n a)\u00a017428 cubic cm<\/p>\n b)\u00a017248 cubic cm<\/p>\n c)\u00a017244 cubic cm<\/p>\n d)\u00a017444 cubic cm<\/p>\n e)\u00a0None of these<\/p>\n 5)\u00a0Answer\u00a0(B)<\/strong><\/p>\n Solution:<\/b><\/p>\n Total surface area of cylinder<\/p>\n => $2 \\pi r h + 2 \\pi r^2 = 3696$<\/p>\n => $2 \\pi r (r + h) = 3696$<\/p>\n $\\because (r + h) = 42$ \u00a0 [Given]<\/p>\n => $2 \\times \\frac{22}{7} \\times r \\times 42 = 3696$<\/p>\n => $44 \\times 6 \\times r = 3696$<\/p>\n => $r = \\frac{3696}{44 \\times 6} = 14$ cm<\/p>\n => $h = 42 – 14 = 28$ cm<\/p>\n $\\therefore$ Volume of cylinder = $\\pi r^2 h$<\/p>\n = $\\frac{22}{7} \\times 14 \\times 14 \\times 28$<\/p>\n = $17248 cm^3$<\/p>\n Question 6:\u00a0<\/b>The respective ratio of radii of two right circular cylinders (A and B) is 4 : 5. The respective ratioof volume of cylinders A and B is 12 : 25. What is the respective ratio of the heights of cylinders A and B ?<\/p>\n a)\u00a02 : 3<\/p>\n b)\u00a03 : 5<\/p>\n c)\u00a05 : 8<\/p>\n d)\u00a04 : 5<\/p>\n e)\u00a03 : 4<\/p>\n 6)\u00a0Answer\u00a0(E)<\/strong><\/p>\n Solution:<\/b><\/p>\n Volume of a cylinder =$\\pi r^2 h$
\nThe length ,breadth and height of a rectangular piece of wood in the 4cm,3cm, 5cm respectively
\nOpposite side of 5cm x 4 cm pieces are coloured in red colour
\nOppsite sides 4cm x 3 cm ,are cloured in blue
\nRest 5 cm x 3 cm are coloured in green in both sides
\nNow the piece is cut in such way that a cuboid of 1cm x 1cm x 1cm will be made<\/p>\n![](\"https:\/\/cracku.in\/media\/uploads\/9984.PNG\")
<\/figure>\n![](\"https:\/\/cracku.in\/media\/uploads\/9984_TQAAUqx.PNG\")
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<\/figure>\n
\n<\/span><\/span><\/span><\/span>where r and h are the radius and height of the cylinder respectively.
\nThe ratio of volumes and ratio of radii of the two cylinders is given.
\nRatio of square of their radii = 16 : 25
\nTherefore the ratio of their heights $h_1$ : $h_2$ = $12 \\times 25$ : $16 \\times 25$
\nwhere $h_1$ and $h_2$ are the heights of two cylinders.
\nthe ratio of their heights = 12 : 16 = 3 : 4
\nOption E is the correct answer<\/p>\n