# Geometry Questions and Answers updated daily – Aptitude

Geometry Questions: Solved 321 Geometry Questions and answers section with explanation for various online exam preparation, various interviews, Aptitude Category online test. Category Questions section with detailed description, explanation will help you to master the topic.

## 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

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

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

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

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

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,

Volume,

**V = x r**= (22/7) x 3 x 3 x 14 = 22 x 9 x 2 = 44 x 9 V = 396 cu m^{2}x h V
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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.

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

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) =

=> (10

Park is in the shape of Square, so area of park (in shape of Square) =

**(Diagonal**^{2}) / 2=> (10

^{2})/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 => x

Larger diagonal = 2x =>2 X 16 = 32cm

Second diagonal = d1 * 2 = 2x cm

Area of rhombus = 1/2 d1 .d2 =>1/2 d1 .d2 = 256 =>1/2 * x * 2x = 256 => x

^{2}= 256 =>x = √256 = 16 cmLarger 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

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

**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

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

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

=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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