Geometry and Trigonometry MCQ Quiz in मल्याळम - Objective Question with Answer for Geometry and Trigonometry - സൗജന്യ PDF ഡൗൺലോഡ് ചെയ്യുക

Last updated on Apr 10, 2025

നേടുക Geometry and Trigonometry ഉത്തരങ്ങളും വിശദമായ പരിഹാരങ്ങളുമുള്ള മൾട്ടിപ്പിൾ ചോയ്സ് ചോദ്യങ്ങൾ (MCQ ക്വിസ്). ഇവ സൗജന്യമായി ഡൗൺലോഡ് ചെയ്യുക Geometry and Trigonometry MCQ ക്വിസ് പിഡിഎഫ്, ബാങ്കിംഗ്, എസ്എസ്‌സി, റെയിൽവേ, യുപിഎസ്‌സി, സ്റ്റേറ്റ് പിഎസ്‌സി തുടങ്ങിയ നിങ്ങളുടെ വരാനിരിക്കുന്ന പരീക്ഷകൾക്കായി തയ്യാറെടുക്കുക

Latest Geometry and Trigonometry MCQ Objective Questions

Top Geometry and Trigonometry MCQ Objective Questions

Geometry and Trigonometry Question 1:

qImage66f3013a3d34df42c82d4e21

The circle above with center O has a circumference of 40.

What is the length of minor arc \(\rm \overparen{A C}\) ?

A. 9

B. 10

C. 18

D. 36

  1. 1
  2. 2
  3. 3
  4. 4

Answer (Detailed Solution Below)

Option 2 : 2

Geometry and Trigonometry Question 1 Detailed Solution

Choice B is correct. A circle has 360 degrees of arc. In the circle shown, O is the center of the circle and ∠AOC is a central angle of the circle. From the figure, the two diameters that meet to form ∠AOC are perpendicular, so the measure of ∠AOC is 90°.

Therefore, the length of minor arc \(\rm \overparen{A C}\) is \(\frac{90}{360}\) of the circumference of the circle.

Since the circumference of the circle is 40, the length of minor arc \(\rm \overparen{A C}\) is \(\frac{90}{360} \times 40=10\)  

Geometry and Trigonometry Question 2:

qImage66f3013a3d34df42c82d4e21

The circle above with center O has a circumference of 64.

What is the length of minor arc \(\rm \overparen{A C}\) ?

A. 16

B. 12

C. 18

D. 36

  1. 1
  2. 2
  3. 3
  4. 4

Answer (Detailed Solution Below)

Option 1 : 1

Geometry and Trigonometry Question 2 Detailed Solution

Choice A is correct. A circle has 360 degrees of arc. In the circle shown, O is the center of the circle and ∠AOC is a central angle of the circle. From the figure, the two diameters that meet to form ∠AOC are perpendicular, so the measure of ∠AOC is 90°.

Therefore, the length of minor arc \(\rm \overparen{A C}\) is \(\frac{90}{360}\) of the circumference of the circle. Since the circumference of the circle is 64, the length of minor arc \(\rm \overparen{A C}\) is \(\frac{90}{360} \times 64= 16\)

Choices B, C, and D are incorrect. The perpendicular diameters divide the circumference of the circle into four equal arcs; therefore, minor arc \(\rm \overparen{A C}\) is \(\frac{1}{4}\) of the circumference. However, the lengths in choices B and C are, respectively, \(\frac{1}{3}\) and \(\frac{1}{2}\) the circumference of the circle, and the length in choice D is the length of the entire circumference. None of these lengths is \(\frac{1}{4}\) the circumference. 

Geometry and Trigonometry Question 3:

qImage66f2f3ec2c1c7c2a445c0f37

The glass pictured above can hold a maximum volume of 664 cubic centimeters, whic. What is the value of k, in centimeters?

A. 2.52

B. 7.67

C. 11.32

D. 10.11

  1. 1
  2. 2
  3. 3
  4. 4

Answer (Detailed Solution Below)

Option 3 : 3

Geometry and Trigonometry Question 3 Detailed Solution

Choice 4 is correct. Using the volume formula \(V=\frac{7 \pi k^3}{48}\) and the given information that the volume of the glass is 473 cubic centimeters, the value of k can be found as follows:

\(664=\frac{7 \pi k^3}{48}\)

\(k^3=\frac{664(48)}{7 \pi}\)

\(k=\sqrt[3]{\frac{664(48)}{7 \pi}} \approx 11.3151\)

Therefore, the value of k is approximately 11.32 centimeters.

Geometry and Trigonometry Question 4:

qImage66f2f3ec2c1c7c2a445c0f37

The glass pictured above can hold a maximum volume of 400 cubic centimeters. What is the value of k, in centimeters?

A. 9.56

B. 7.67

C. 7.79

D. 10.11

  1. 1
  2. 2
  3. 3
  4. 4

Answer (Detailed Solution Below)

Option 1 : 1

Geometry and Trigonometry Question 4 Detailed Solution

Choice 1 is correct.

Using the volume formula \(V=\frac{7 \pi k^3}{48}\) and the given information that the volume of the glass is 400 cubic centimeters, the value of k can be found as follows:

\(400=\frac{7 \pi k^3}{48}\)

\(k^3=\frac{400(48)}{7 \pi}\)

\(k=\sqrt[3]{\frac{400(48)}{7 \pi}} \approx 9.556\)

Therefore, the value of k is approximately 9.56 centimeters.

Geometry and Trigonometry Question 5:

qImage6752f4d84fa3e897754011ec

The figure shows the lengths, in centimeters cm, of the edges of a right rectangular prism. The volume V of a right rectangular prism is ℓwh, where ℓ is the length of the prism, w is the width of the prism, and h is the height of the prism. What is the volume, in cubic centimeters, of the prism?

A. 160

B. 240

C. 120

D. 110

  1. 1
  2. 2
  3. 3
  4. 4

Answer (Detailed Solution Below)

Option 1 : 1

Geometry and Trigonometry Question 5 Detailed Solution

Choice 1 is correct.

It's given that the volume of a right rectangular prism is ℓwh. The prism shown has a length of 5 cm, a width of 8 cm, and a height of 4 cm .

Thus, ℓwh = (5)(8)(4), or 160 cubic centimeters.

 

Geometry and Trigonometry Question 6:

qImage6752f3e815cc5efda6ba17c7

The figure shows the lengths, in centimeters cm, of the edges of a prism. The volume V of a right rectangular prism is ℓwh, where ℓ is the length of the prism, w is the width of the prism, and h is the height of the prism. What is the volume, in cubic centimeters, of the prism?

A. 360

B. 240

C. 120

D. 250

  1. 1
  2. 2
  3. 3
  4. 4

Answer (Detailed Solution Below)

Option 4 : 4

Geometry and Trigonometry Question 6 Detailed Solution

Choice 4 is Correct.

It's given that the volume of a prism is ℓwh. The prism shown has a length of 5 cm, a width of 5 cm, and a height of 10 cm.

Thus, ℓwh = (5)(5)(10), or 250 cubic centimeters.

Geometry and Trigonometry Question 7:

qImage6752f278b38dfe8153af8764

The figure shows the lengths, in centimeters cm, of the edges of a right rectangular prism. The volume V of a right rectangular prism is ℓwh, where ℓ is the length of the prism, w is the width of the prism, and h is the height of the prism. What is the volume, in cubic centimeters, of the prism?

A. 36

B. 24

C. 66

D. 11

  1. 1
  2. 2
  3. 3
  4. 4

Answer (Detailed Solution Below)

Option 3 : 3

Geometry and Trigonometry Question 7 Detailed Solution

Choice 3 is correct.

It's given that the volume of a right rectangular prism is ℓwh. The prism shown has a length of 11 cm, a width of 2 cm, and a height of 3 cm .

Thus, ℓwh = (11)(2)(3), or 66 cubic centimeters.

Geometry and Trigonometry Question 8:

The triangle shown has a perimeter of 25 units. If x = 10 units and y = 8 units, what is the value of z, in units?

qImage66f2ec2596db16bfb14318b0

A. 6

B. 7

C. 9

D. 16

  1. 1
  2. 2
  3. 3
  4. 4

Answer (Detailed Solution Below)

Option 2 : 2

Geometry and Trigonometry Question 8 Detailed Solution

Choice 2 is correct.

The perimeter of a triangle is the sum of the lengths of its three sides. The triangle shown has side lengths x, y, and z. It's given that the triangle has a perimeter of 25 units. Therefore, x + y + z = 25. If x = 10 units and y = 8 units, the value of z, in units, can be found by substituting 10 for x and 8 for y in the equation x + y + z = 25, which yields 10 + 8 + z = 25, or 18 + z = 25. Subtracting 18 from both sides of this equation yields z = 7.

Therefore, if x = 10 units and y = 8 units, the value of z, in units, is 7.

 

Geometry and Trigonometry Question 9:

The triangle shown has a perimeter of 20 units. If x = 8 units and y = 5 units, what is the value of z, in units?

qImage66f2ec2596db16bfb14318b0

A. 6

B. 7

C. 9

D. 16

  1. 1
  2. 2
  3. 3
  4. 4

Answer (Detailed Solution Below)

Option 2 : 2

Geometry and Trigonometry Question 9 Detailed Solution

Choice 2 is correct.

The perimeter of a triangle is the sum of the lengths of its three sides. The triangle shown has side lengths x, y, and z. It's given that the triangle has a perimeter of 20 units. Therefore, x + y + z = 20. If x = 8 units and y = 5 units, the value of z, in units, can be found by substituting 8 for x and 5 for y in the equation x + y + z = 20, which yields 8 + 5 + z = 20, or 13 + z = 20. Subtracting 16 from both sides of this equation yields z = 7.

Therefore, if x = 8 units and y = 5 units, the value of z, in units, is 7 .

Geometry and Trigonometry Question 10:

The triangle shown has a perimeter of 32 units. If x = 13 units and y = 10 units, what is the value of z, in units?

qImage66f2ec2596db16bfb14318b0

A. 6

B. 7

C. 9

D. 16

  1. 1
  2. 2
  3. 3
  4. 4

Answer (Detailed Solution Below)

Option 3 : 3

Geometry and Trigonometry Question 10 Detailed Solution

Explanation:

The perimeter of a triangle is the sum of the lengths of its three sides. The triangle shown has side lengths x, y, and z. It's given that the triangle has a perimeter of 32 units.

Therefore, x + y + z = 32. If x = 13 units and y = 10 units, the value of z, in units, can be found by substituting 13 for x and 10 for y in the equation x + y + z = 32, which yields 13 + 10 + z = 32, or 23 + z = 32. Subtracting 23 from both sides of this equation yields z = 9.

Therefore, if x = 13 units and y = 10 units, the value of z, in units, is 9.

Hence Option(3) is correct.

 

Get Free Access Now
Hot Links: teen patti master update teen patti 500 bonus teen patti master 2024