SSC CGL MENSURATION MCQ ENGLISH

Correct Answer : Final_Correct_Answer

Explanation : Explanation

Correct Answer : (D)

Explanation : We know that,The volume of cone =13πr2hWhere r is the base radius, and h is the height.% Change =[(Final value – Initial value)Initial value]×100Let the initial volume be V1 .By using the above formula,V1=13πr2h…(1)Now h is increased by 100% . Then,New height =h(1+100100)=2hSo, the new volume,V2=13πr2×2h…(2)So, % change in volume,ΔV=V2−V1V1×100⇒ΔV=13πr2(2h)−13πr2h13πr2h×100⇒ΔV=2h−hh×100⇒ΔV=100%

Correct Answer : (C)

Explanation : Volume of big sphere =n× Volume of small sphereV=43πr343π(10)3=n×43π(2)310×10×10=n×2×2×21000=n×8n=125

Correct Answer : (B)

Explanation : Given:Diameter of cylinder =8 mHeight of cone =15 mHeight of cylinder =12 mWe know that,Area of canvas required for the tent = Curved surface area of the cylindrical portion + Curved surface area of the coneCurved surface area of cylinder =2πrh=2(π)×4×12=96(π)According to the question,Height (h) of the cone = Height of the vertex from the ground − Height of the cylinder=15−12=3 mSlant height =(32+42)=5 mCurved surface area of cone =π×r×l=π(4)(5)=20π∴ Area of canvas =(96π+20π)=116π

Correct Answer : (B)

Explanation : Given:A lawn in the shape of a rectangle has an area of 7260 m 2 and its sides are in the ratio 5:3 . Its perimeter is equal to the perimeter of a circular garden.As we know,Area of a rectangle =l×bPerimeter of a rectangle =2(l+b)Area of a circle =πr2Perimeter of a circle =2πrLet the sides of the rectangle be 5x and 3x .Now,5x×3x=7260⇒15×2=7260⇒x2=726015⇒x2=484⇒x=22So, sides are 5×22=110 m and 3×22=66 mAccording to the question,2(110+66)=2πr⇒πr=176⇒r=176×722⇒r=56Now,Area of the circular garden =(227)×562=22×8×56=9856 m 2

Correct Answer : (D)

Explanation : Given:Radius (r1) of hemisphere =4.2 cmRadius (r2) of cylinder =6 cmHeight (h)= ?The object fromed by recasting the hemisphere will be same in volume. So, Volume of sphere = Volume of cylinder43πr13=πr22 h⇒43π×(4.2)3=π(6)2 h⇒43×4.2×4.2×4.236=hh=(1.4)3=2.74 cmTherefore, the height of cylinder so formed will be 2.74 cm.

Correct Answer : (C)

Explanation : Given,Let, x be the edge of the large cube.Egde of the cube can determine by adding cubes of sides.x3=33+43+53⇒x3=27+64+125=216⇒x=2163⇒x=6 cm∴ Required ratio = Total surface area of smaller cubes Surface area of larger cubes=6(3)2+6(4)2+6(5)26(6)2=6×9+6×16+6×256×36=54+96+150216=300216=2518=25:18

Correct Answer : (A)

Explanation : Given,The ratio of the radii of two cones is 5:6 and their volumes are in the ratio 8:9 .As we know,Volume of the cone =13(πr2h)Let the radius of one cone is 5r and another cone is 6r and their height is h1 and h2 respectively.The ratio of their volume is:13(π×25r2×h1):13(π×36r2×h2)=25h1:36h2But, The ratio of their volume is equal to 8:9 , then:25h1:36h2=8:9⇒h1:h2=(8×36):(25×9)⇒h1:h2=32:25∴ The ratio of height of the two cone is 32:25 .

Correct Answer : (C)

Explanation : The length and breadth of a rectangle are in the ratio 7:4 . Let the length of the rectangle (l)=7kBreadth of the rectangle (b)=4kPerimeter of the rectangle (P)=220cm⇒2×(l+b)=220cm⇒2×(7k+4k)=220⇒2×11k=220⇒k=10cmLength of the rectangle (l)=7k=70cmBreadth of the rectangle (b)=4k=40cmArea of the rectangle (A)=l×b=70×40=2800cm2

Correct Answer : (D)

Explanation : Let the volume of original cone be V .⇒V=13πr2hNow, the height is tripled and radius is doubled,⇒h′=3h and r′=2r⇒ New volume,V′=13πr′2h′=13π(2r)2(3h)=4πr2hSo, as per question,⇒VV′=4πr2h13πr2h=121=12:1∴ The ratio of the volume of new cone to the original one =12:1

Correct Answer : (A)

Explanation : Ratio of radius of a circle and side of a square =2:3Breadth of the rectangle = Side of squareLength of the rectangle =37th × Breadth of the rectanglePerimeter of the rectangle =102 cmPerimeter of square =4× SidePerimeter of rectangle =2( length + breadth )Area of square = side 2Area of rectangle = length × breadthSuppose the length of the rectangle and breadth of the rectangle is 10x and 7x , respectively.⇒2(10x+7x)=102⇒17x=51⇒x=3Length of the rectangle =30 cmBreadth of the rectangle =21 cm∴ Side of the square =21 cmThe ratio of the radius of a circle and the side of a square is 2:3⇒2(10x+7x)=102 ⇒17x=51⇒2 unit =14 cmThe radius of the circle is 14 cmSo, the area of the circle =π(14)2=227×14×14=616 sq. cm

Correct Answer : (D)

Explanation : The sides of triangles are 6 cm,8 cm and 10 cmS=6+8+102=242=12Area of triangle =12(12−6)(12−8)(12−10)=24sq.cmWidth of rectangle 8 cmWe know that,Length =AreaBreadth∴ Length = 248=3 cm∴ Perimeter =2(8+3)cm=22 cm

Correct Answer : (A)

Explanation : Given:The radius of the base of a right circular cone is 15 cm.The total surface area is 480π cm 2 .We know that,The total surface area =πrl+πr2The volume of the right circular cone =13πr2hThe slant height of the cone, l=h2+r2The total surface area,πrl+πr2=480π⇒π(rl+r2)=480π⇒(15×l+152)=480⇒15×l+225=480⇒15×l=255⇒l=17 cmThe slant height of the cone =17 cml2=r2+h2⇒172=152+h2⇒289=225+h2⇒h2=64⇒h=8 cmNow,The volume of the right circular cone =13π×152×8=600π cm 3

Correct Answer : (D)

Explanation : Radius of steel sphere R=6 cmRadius of small balls r=1 cmAs we know,Volume of sphere =(43)×πr3Let n balls each of radius 1 cm be made from steel sphere.According to the question,(43)×πR3=n×(43)×πr3⇒6×6×6=n×1×1×1⇒n=216

Correct Answer : (D)

Explanation : Given,Length =15cmBreadth =12cmHeight =11cmAs we know,The total area of the four side faces of cuboid =2h(l+b)The total area of the four side faces of cuboid =2×11(12+15)=22×27=594cm2Now, converting percentage to fraction to make calculation easy.623%=115,813%=112Length after decrease =15×1415=14cmBreadth after increase =12×1312=13cmHeight (no change) =11cmThe total area of the four side faces after change in length and breadth =2×11(14+13)=22×27=594cm2Change in total area =594−594=0∴ No change in the total area of the four side faces.

Correct Answer : (C)

Explanation : For Statement l:Total Surface area of cuboid =2(lb+bh+hl)Let Length be 3x , breadth =2x , height =x⇒352=2(3x×2x+2x×x+x×3x)⇒176=(6×2+2×2+3×2)⇒176=11×2⇒x2=16⇒x=4∴ Length =12 , Breadth =8 , Height =4∴ Volume =lbh⇒12×8×4⇒384cm3Statement I alone is not sufficient to answer the question.For statement II:Total Surface Area of Cube =6s2⇒384=6s2⇒s2=64⇒s=8∴ Volume of the cube =s3⇒83⇒512cm3Statement II alone is not sufficient to answer the question.For Statement III:Height of the cuboid =xcmLength =3xBreadth =2x∴ Difference =3x−x⇒8=2x⇒x=4∴ Length =12 , Breadth =8 , Height =4∴ Volume =lbh⇒12×8×4⇒384cm3Statement III alone is not sufficient to answer the question.But we can solve the question by either Statement I and II or statement II and III.

Correct Answer : (C)

Explanation : Let the radius of the base of the cylindrical room be r .Let the height be h .The area of the floor is πr2The volume of the room is πr2hThe area of the wall is 2πrh .Given:Capacity of room =3140m3Cost of painting the floor = Rs. 3140The area of the floor =314010=314m2πr2=314⇒r=10mThe volume of the room is 3140m3πr2h=3140⇒h=10mSo, The area of the curved surface within the room =2πrh=628m2Therefore, The cost of painting this =10×628= Rs. 6280

Correct Answer : (A)

Explanation : Given:Length of a rectangle (l)=24 cm and Diagonal =25 cmLet the breadth of the rectangle =b mApplying Pythagoras Theorem in triangle ABC ,We get, (AC)2=(AB)2+(BC)2⇒(25)2=(24)2+(b)2⇒625=576+(b)2⇒625−576=b2⇒49=b27×7=b∴b=7 cmNow, perimeter of the rectangle=2(l+b)=2(24+7)=2(31)=62 cm

Correct Answer : (C)

Explanation : Given:The curved surface area of the right cylinder =3696 cm2Height of cylinder =3× radius of the cylinderAs we know,The curved surface area of cylinder =2πrhVolume of cylinder =πr2hWhere,r= radius of cylinderh= height of cylinder1 cm3=0.001 litreLet the radius of the cylinder be ‘ r ‘ and the height of the cylinder be ‘ h ‘.Curved surface area of cylinder =2πrh⇒2πrh=3696⇒2πr×3r=3696(h=3r)⇒r2=(3696×7)(22×6)⇒r2=196⇒r=14 cm⇒h=3r=3×14=42 cmVolume of cylinder =πr2h=(227)×14×14×42=25872 cm3We know, 1 cm3=0.001 litre=25872×0.001=25.872 litres∴ The volume of the cylinder is 25.872 litres.

Correct Answer : (D)

Explanation : We know that,The Volume of cone =πr2h3 , where r and h are the radius and height of the cone respectively.The volume of the cone with certain radius is one-third of the area of the base times of the height.

Correct Answer : (A)

Explanation : The volume of the cone will be maximum if the height and the radius of the cone are the same as that of the cylinder.Let the height and radius of the cylinder be h,r and l be slant height respectively.As, we knowl2=h2+r2h=252−72h=24 cmVolume of cylinderV=πr2h=π×72×24=1176πcm3

Correct Answer : (D)

Explanation : Area of plot ABCD = Area of ADE + Area of AFB + Area of BCEF= 12 × 50 × 120 + 12 × 40 × 30 + 40 × 90= 3000 + 600 + 3600= 7200 sq.m

Correct Answer : (B)

Explanation : Let, radius of the cylinder = r cm.Height of the cylinder = h cm.According to problem,⇒ r + h = 35 —— (1)⇒ 2πr(r + h) = 1540 —– (2)Substituting the value of equation (1) in equation (2), we get,⇒ 2πr × 35 = 1540⇒ 2πr = 44⇒ 2 × 227 × r = 44⇒ r = 7From equation (1) we get,⇒ 7 + h = 35⇒ h = 28∴ Volume of the cylinder = πr2h= 227 × 72 × 28= 4312 cubic cm

Correct Answer : (B)

Explanation : Given:The ratio between the length and the breadth of a rectangular park is 3:2Formula used:Perimeter of the Rectangle (park) =2(l+b)Where, l= length and b= breadthTo convert km/hr into m/sec , multiply the number by 518Distance covered in 8 minutes, with the speed 12km/hr=12×518×8×60=1600mLet the length and breadth of rectangular park be 3x and 2xPerimeter of the park =2(3x+2x)⇒2(3x+2x)=1600⇒5x=16002⇒x=8005⇒x=160Area of the park =3x×2x=6×2=6×160×160=153600m2∴ Area of the park is 153600m2

Correct Answer : (A)

Explanation : Given:Side of square =32 cmHeight of pyramid =30 cmWe know that,Total surface area of pyramid =12× Base Perimeter × slant height + Base AreaPerimeter of square =4× SideArea of square = (side) 2Now,Side of square (a)=32 cmPerimeter of square =4×32=128Area of square =(32)2=1,024In the figure,OR=12× side of square⇒12×32=16 cmHeight (h)=OP=30 cmIn △POR ,(PR)2=(OR)2+(OP)2⇒(PR)2=(16)2+(30)2⇒(PR)=256+900⇒PR=34So, Slant height (I)=PR=34 cmNow,Total Surface Area of Pyramid =12×128×34+1024⇒3200 cm 2

Correct Answer : (D)

Explanation : Given:Diameter of sphere =16cmDiameter of balls =2cmAccording to the question,Radius of the sphere =162=8cmSo, volume of the sphere =(43)×πr3=((43)×(227)×8×8×8)cm3Now,Number of balls=volume of spherevolume of ball=((43)×(227)×8×8×8)((43)×(227)×1×1×1)=8×8×8=512∴ The number of balls of diameter 2cm each, that can be made from a sphere of diameter 16cm are 512 .

Correct Answer : (A)

Explanation : Given,Volume of the gold brick =18×48×16=13824 cm 3As we know,Volume of the cubical shape =A3⇒A3=13824 cm 3⇒A=138243⇒A=24 cm

Correct Answer : (D)

Explanation : Given,The radius of a sphere is increased by 2.5 decimeter (dm), then its surface area increases by 110 dm 2 .As we know,The surface area of sphere =4πr2The volume of sphere =(43)×πr3Where r= radius and π=227a2−b2=(a+b)(a−b)according to the question,4π(r+2.5)2−4πr2=110⇒4π[(r+2.5)2−r2]=110⇒4π[(r+2.5+r)(r+2.5−r)]=110⇒4×227×(2r+2.5)×2.5=110⇒10×(2r+2.5)=35⇒20r+25=35⇒r=12 dmNow,Volume =43×π×(12)3⇒43×227×18⇒88168=1121 dm 3∴ The volume of the sphere is 1121 dm 3 .

Correct Answer : (C)

Explanation : Let the angle between the generator and the axis of the cone be ‘θ’, shown below,Radius of cone = OB = r (let)When the semi-circle is rolled to form a cone, slant height of cone = Radius of semi-circleAB = R (let)Also, the circumference of the base of cone = Circumference of semi-circle2πr = πR⇒ rR=12Now, considering ∆OAB,⇒ sin θ = OBAB=rR⇒ sin θ = 12⇒ sin θ = sin 30°∴ θ = 30°

Correct Answer : (C)

Explanation : Given:Sides of the triangle are 25 cm, 39 cm and 56 cmWe know that,Semi perimeter, s=a+b+c2s=(25+39+56)2=60 cmArea =s(s−a)(s−b)(s−c)=60(60−25)(60−39)(60−56)=60×35×21×4=420 cm 2Area of triangle =12× base × height⇒ Area of triangle =12×56× height⇒420=28× height⇒ Height =42028=15 cm∴ The perpendicular from the opposite vertex on the side of 56 cm is 15 cm.

Correct Answer : (B)

Explanation : We know that,Pythagoras Theorem: In a right-angle triangle (triangle in which one angle is 90∘ )Base 2+ Perpendicular 2= Hypotenuse 2Given:r=l=8 cmLet, the slant height be h cm.Using the Pythagoras theorem,h2=82+82⇒h2=2×82Taking square root on both sides,h=(2×82)⇒h=82 cm∴ The slant height of the cone is 82 cm.