Enroll to CMAT 2023 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>If the volume and curved surface area of a cylinder are 616 $m^3$ and 352 $m^2$ respectively what is the total surface area of the cylinder (in $m^2$)<\/p>\n a)\u00a0429<\/p>\n b)\u00a0419<\/p>\n c)\u00a0435<\/p>\n d)\u00a0421<\/p>\n e)\u00a0417<\/p>\n 6)\u00a0Answer\u00a0(A)<\/strong><\/p>\n Solution:<\/b><\/p>\n Volume of a cylinder=$\\pi \\times r^{2} \\times h$ <\/p>\n <\/p>\n <\/p>\n <\/p>\n Question 7:\u00a0<\/b>The sum of the radius and height of a cylinder is 18 metre. The total surface area of the cylinder is 792 sq. metre, what is the volume of the cylinder ? (in cubic metre)<\/p>\n a)\u00a01848<\/p>\n b)\u00a01440<\/p>\n c)\u00a01716<\/p>\n d)\u00a01724<\/p>\n e)\u00a01694<\/p>\n 7)\u00a0Answer\u00a0(E)<\/strong><\/p>\n Solution:<\/b><\/p>\n let the height and radius of cylinder be H mtr and R mtr<\/p>\n R + H = 18<\/p>\n total surface area of cylinder = 2$\\barwedge$RH + 2$\\barwedge(R)^2$ = 792<\/p>\n R(H + R) = $\\frac{792×7}{22×2}$<\/p>\n R = 7 mtr<\/p>\n H = 18-7 = 11 mtr<\/p>\n volume = $\\frac{22}{7}(R)^2(H)$<\/p>\n Volume = 1694 cubic mtr<\/p>\n Question 8:\u00a0<\/b>The respective ratio of curved surface area and total surface area of a cylinder is 4:5. If the curved surface area of the cylinder is 1232 cm2, what is the height ? (in cm)<\/p>\n a)\u00a028 cm<\/p>\n b)\u00a034 cm<\/p>\n c)\u00a036 cm<\/p>\n d)\u00a030 cm<\/p>\n e)\u00a0None of these<\/p>\n 8)\u00a0Answer\u00a0(A)<\/strong><\/p>\n Solution:<\/b><\/p>\n Let R and H be the radius and height of cylinder<\/p>\n Curved Surface area of cylinder = 2$\\barwedge$RH = 1232<\/p>\n ($\\barwedge$RH= 616 sqr cm)<\/p>\n Total surface area of cylinder = 2$\\barwedge$RH + 2$\\barwedge(R)^2$ = 2$\\barwedge$R(H+R)<\/span><\/p>\n it is given that CurvedSurfaceArea\/TotalSurfaceArea = 4\/5<\/span><\/p>\n 1232\/(1232\u00a0+ 2$\\barwedge(R)^2$)<\/span> = 4\/5<\/span><\/p>\n R = 7 cm <\/span><\/p>\n 2$\\barwedge$RH = 1232 2$\\barwedge$7H = 1232<\/p>\n 44H =1232<\/span> \u00a0<\/span><\/p>\n \u00a0<\/span><\/p>\n Question 9:\u00a0<\/b>A right circular cylindrical tank has the storage capacity of 98808 ml. If the radius of the base of the cylinder is three-fourth of the height, what is the diameter of the base ?<\/p>\n a)\u00a028 cms<\/p>\n b)\u00a056 cms<\/p>\n c)\u00a021 cms<\/p>\n d)\u00a058 cms<\/p>\n e)\u00a0None of these<\/p>\n 9)\u00a0Answer\u00a0(D)<\/strong><\/p>\n Solution:<\/b><\/p>\n Volume if cylinder = \u03c0$(R)^2$h<\/p>\n R is the radius and h is the height of cylinder<\/p>\n Volume = 98808 ml<\/p>\n It is given that R = $\\frac{3}{4}$h<\/p>\n $\\frac{4}{3}$ $(R)^3$ \u03c0 = 98808<\/span><\/p>\n R = 28.68 <\/span><\/span><\/p>\n Diameter = 28.68 \u00d7 2 ~58<\/span><\/span><\/p>\n Question 10:\u00a0<\/b>The edge of an ice cube is 14 cm. The volume of the largest cylindrical ice cube that can be fit into it?<\/p>\n a)\u00a02200 cu. cm<\/p>\n b)\u00a02000 cu. cm<\/p>\n c)\u00a02156 cu. cm<\/p>\n d)\u00a02400 cu. cm<\/p>\n e)\u00a0None of these<\/p>\n 10)\u00a0Answer\u00a0(C)<\/strong><\/p>\n Solution:<\/b><\/p>\n Radius of the cylinder = r =\u00a0$\\frac{14}{2}$ = 7
\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\")
<\/figure>\n![](\"https:\/\/cracku.in\/media\/uploads\/9984_UcxL21R.PNG\")
<\/figure>\n![](\"https:\/\/cracku.in\/media\/uploads\/9984_sITUqT2.PNG\")
<\/figure>\n
\nwhere $r$ and $h$ are the radius and height of the cylinder.
\n$\\pi \\times r^{2} \\times h$ = $616 m^{3}$
\nCurved Surface Area of Cylinder=$2\\times \\pi \\times r \\times h$=$352 m^{2}$
\n$\\pi \\times r \\times h$=$176$
\nReplacing $\\pi \\times r \\times h$ in Volume formula we get,
\n$ r \\times 176$=$616$
\n$r=3.5 m$
\nTotal Surface Area = Curved Surface Area + 2$\\times$ Area of base
\n=$352 + 2\\times pi \\times r^{2}$
\n=$352 + 2\\times pi \\times 3.5^{2}$
\n=$352+77$
\n=$429 m^{2}.$
\nHence Option A is the correct answer.<\/span><\/span><\/span><\/span><\/span><\/p>\n
\n<\/span><\/p>\n
\n<\/span>H = 28 cm<\/span><\/p>\n
\nHeight of the cylinder = h =14
\nVolume = Pi x r2\u00a0<\/sup>x h
\n=\u00a0$\\frac{22}{7}$ x 7 x 7 x 14 = 2156<\/p>\n