Geometry Questions and Answers updated daily – Aptitude

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Geometry Questions

301. Find the curved surface area of a cylinder of length 7 m and a base of radius 3 meter.




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Correct Ans:132
Explanation:
Let r and h be the radius and height of the cylinder respectively.
r = 3 and h = 7
Curved Surface area , CSA = 2 x pi x r x h CSA = 2 x (22/7) x 3 x 7 = 132 sq m
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302. Find the length of the diagonal of a cuboid 12m long, 9 m broad and 8 m high.




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Correct Ans:17
Explanation:
Let l, b and h be the length, breadth and height of the cuboid respectively.
Diagonal = sqrt(lxl + bxb + hxh) = sqrt(12 x 12 + 9 x 9 + 8 x 8) = sqrt(144+81+64) Diagonal = sqrt(289) = 17
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303. Sum of all external angles in any triangle is  ______ degrees.




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Correct Ans:360
Explanation:
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304. Find the perimeter of the rectangle having length 24 cm and breadth 21 cm.




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Correct Ans:90
Explanation:
Given length of the rectangle, l = 24 cm Breadth of the rectangle, b= 21 cm Perimeter of the rectangle is, P = 2(l+b) P = 2 x (24 + 21) cm P = 2 x 45 = 90 cm
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305. Find the curved surface area of a cylinder of length 7 m and a base of radius 4 meter.




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Correct Ans:176
Explanation:
Let r and h be the radius and height of the cylinder respectivley. r = 4 and h = 7 Curved Surface area , CSA = 2 x pi x r x h CSA = 2 x (22/7) x 4 x 7 = 176 sq m
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306. Area of the base of a cuboid 49 sq m, area of side face and other side face are 64 sq m and 25 sq m respectively. Find the volume of the cuboid




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Correct Ans:280
Explanation:
Let l, b and h be the length, breadth and height of the cuboid respectively. According to given data, Area of the base of a cuboid = l x b = 49 , ----> (1) Area of the one side face = b x h = 64 ------> (2) Area of the other side face = h x l = 25 -----> (3) On multiplying the above equations we get l x b x b x h x l x h = 49 x 64 x 25 => (l x b x h)^2 = 49 x 64 x 25 => l x b x h = 7 x 8 x 5 = 280 Volume of the cuboid = l x b x h = 280
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307. Find the curved surface area of a cylinder of length 7 m and a base of radius 3 meter.




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Correct Ans:132
Explanation:
Let r and h be the radius and height of the cylinder respectively.
r = 3 and h = 7
Curved Surface area , CSA = 2 x pi x r x h CSA = 2 x (22/7) x 3 x 7 = 132 sq m
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308. Find the length of the diagonal of a cuboid 10m long, 8 m broad and 5 m high.




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Correct Ans:13.75
Explanation:
Let l, b and h be the length, breadth and height of the cuboid respectively.
Diagonal of cuboid = sqrt(lxl + bxb + hxh) = sqrt(10 x 10 + 5 x 5 + 8 x 8) = sqrt(100+25+64) Diagonal = sqrt(189) = 13.75
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309. A tennis court has a length of 29 units, and breadth of 20 units. Find the area of the tennis court ?




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Correct Ans:580
Explanation:
Area of Rectangle = length x breadth
29 x 20= 580
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310. Find the volume of a cube of side 12 cm




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Correct Ans:1728
Explanation:
Let the side of the cube be a Then, Volume of the cube V = a^3 = a x a x a V = 12 x 12 x 12 = 1728 cu cm
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311. Find the volume of the cylinder which has a height of 14 meters and a base of radius 3 meters. ?




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Correct Ans:396
Explanation:
Let r and h be the radius and height of the cylinder.
Volume, V = pix r2 x h V = (22/7) x 3 x 3 x 14 = 22 x 9 x 2 = 44 x 9 V = 396 cu m
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312. Find the volume of a cuboid with dimension 22 cm by 12 cm by 7.5 cm




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Correct Ans:1980
Explanation:
Length of the cuboid be l, breadth of the cuboid be b and height of the cuboid be h.
Volume of the cuboid is, V = l x b x h V = 22 x 12 x 7.5 = 1980 cu cm.
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313. The circumference of a park is 750 m. A and B start walking from the same direction at 6.75 kmph and 4.75 kmph. In what time will they meet each other again?




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Correct Ans:3 hours
Explanation:
Time taken by A to complete one revolution = 750/ (6.75 x 5)/18 sec = (750*18)/(6.75*5)sec.
Time taken by B = (750 x 18)/(4.75 x 5) sec
Time required = LCM of numerators / HCF of denominators = 750 x 1800 / 125 = 1800 x 6 seconds = (1800 x 6)/3600 hrs = 3 hours
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314. Length and breadth of a rectangular plot is 20m & 27m respectively. Find the Difference between Area and Perimeter ?




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Correct Ans:446
Explanation:
Difference between area & perimeter = (length x breadth ) - (2 x (length + breadth) ) = (20 * 27 ) - (2 * (20 + 27) ) = 540 - (2 * 47) = 540 - 94 = 446
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315. Steve walks diagonally in a Square shaped park. Steve covers a distance of 10m. Can you find the area of the Square park  ?




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Correct Ans:50sq.m
Explanation:
Given Steve walks distance of 10m
Park is in the shape of Square, so area of park (in shape of Square) = (Diagonal2) / 2
=> (102)/2 = 50sq.m
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316. The area of rhombus is 256 square cm and one of its diagonal is twice the other in length. Then length of its larger diagonal is  ?




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Correct Ans:32 cm
Explanation:
Let diagonal of Rhombus be d1 = x
Second diagonal = d1 * 2 = 2x cm
Area of rhombus = 1/2 d1 .d2 =>1/2 d1 .d2 = 256 =>1/2 * x * 2x = 256 => x2 = 256 =>x = √256 = 16 cm
Larger diagonal = 2x =>2 X 16 = 32cm
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317. Diameter of a roller is 2.4 m and it is 1.68 m long. If it takes 1000 complete revolutions once over to level a field, then the area of the field is  ?




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Correct Ans:12672 sq m
Explanation:
Given, Diameter of roller = 2.4 m => radius = 2.4 / 2 = 1.2 m
Circumference = 2Π x r = 2Π x1.2 m
Area covered in one revolution = 2.4 Π x 1.68 = 12.672 sq m ;
Total area of the field = 12.672 x 1000 = 12672 sq. m
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318. If perimeter of a rectangle is 180 m and the difference between the length and the breadth is 8 metres, what is the area of the rectangle?




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Correct Ans:2009 sq m
Explanation:
Let x = length of the rectangle and breadth = (x – 8) m
Given , perimeter of the rectangle = 180 m perimeter of the rectangle = 2 * (l+b) => 2(x + x - 8)= 180? => (2x - 8) = 90? =>2x = 90 + 8 = 98 => x = 49 m?
Breadth = 49 – 8 = 41 m
Area of the rectangle = l * b = 49 x 41 = 2009 sq. m
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319. The side of a square is 2 cms less than the length of a rectangle and the breadth of the rectangle is 5 cms less than the side of the square. The area of the square is 324 sq. cms. What is the area of the rectangle?




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Correct Ans:260 sq. cms
Explanation:
Side of a square = ?Area = ?324 = 18 cm
Length of the rectangle = 18 + 2 = 20 cm and breadth = 18 – 5 = 13 cm
Area of rectangle = Length x breadth = 20 x 13 = 260 sq. cm
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320. One of the angles of a right angled triangle is 15°, and the hypotenuse is 1 m. The area of the triangle (in square cm) is




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Correct Ans:1250
Explanation:
Sin 15° = sin (45° – 30°) = sin 45° x cos 30° – cos 45° x sin 30°
=1/√2 x √3/2 – 1/√2 x 1/2
= √3/2√2 – 1/2√2
= (√3 - 1) / 2√2

cos 15° = cos (45° – 30°) = cos 45°. cos 30° + sin 45°. sin 30°
= 1/√2 x√3/2 + 1/√2 x 1/2
=√3/2√2 + 1/2√2
= (√3+1)/2√2;

Let ABC be the right angled triangle
AB = AC sin 15°
= (√3 – 1)/2√2 m

BC =AC cos 15° = (√3+1)/2√2 m

Area of ABC = 1/2 x AB x BC
= (1/2 x (√3 - 1)/ 2√2 x (√3+1)/ 2√2) sq m
= (3 - 1)/16 sq m
= 1/8 sq m
= 10000/8 cm
= 1250 sq cm
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