Quantitative Aptitude

Mensuration

2,507 Questions
All Direct Formula Application 1067 Shape Transformations 343 Mensuration Ratio Equations 277 Combined & Hollow Solids 247 Successive Percentage Changes 178 Inscribed & Circumscribed Figures 165 Cost Estimation Problems 100 Liquid Pour & Submergence 67 Unit Conversions 35 Path & Border Calculations 17 Time & Work Integration 7 Scale & Model Proportions 2

Mensuration Questions

Multiple choice

Find the surface area of a sphere with radius 4 cm.

  1. 251.2 cm²

  2. 125.6 cm²

  3. 62.8 cm²

  4. 31.4 cm²
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The surface area of a sphere is given by SA = 4πr², where r is the radius. In this case, r = 4 cm, so SA = 4π(4²) = 251.2 cm².

Multiple choice

A cylinder has a radius of 6 cm and a height of 8 cm. What is the volume of the cylinder?

  1. 288π cm³

  2. 144π cm³

  3. 72π cm³

  4. 36π cm³
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The volume of a cylinder is given by V = πr²h, where r is the radius and h is the height. In this case, r = 6 cm and h = 8 cm, so V = π(6²)(8) = 288π cm³.

Multiple choice

A cone has a radius of 5 cm and a height of 12 cm. What is the volume of the cone?

  1. 314 cm³

  2. 157 cm³

  3. 78.5 cm³

  4. 39.25 cm³
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The volume of a cone is given by V = ½πr²h, where r is the radius and h is the height. In this case, r = 5 cm and h = 12 cm, so V = ½π(5²)(12) = 314 cm³.

Multiple choice

A sphere has a radius of 4 cm. What is the volume of the sphere?

  1. 268.08 cm³

  2. 134.04 cm³

  3. 67.02 cm³

  4. 33.51 cm³
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The volume of a sphere is given by V = ½πr³, where r is the radius. In this case, r = 4 cm, so V = ½π(4³) = 268.08 cm³.

Multiple choice

A circle has a radius of 10 cm. What is the area of the sector of the circle formed by a central angle of 60 degrees?

  1. 25π cm^2

  2. 50π cm^2

  3. 75π cm^2

  4. 100π cm^2
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The area of a sector of a circle is given by the formula A = (θ/360) * πr^2, where θ is the central angle in degrees and r is the radius of the circle. Substituting the given values, we get A = (60/360) * π(10)^2 = 25π cm^2.

Multiple choice

What is the area of a circle with radius 10 cm?

  1. 100π cm^2

  2. 200π cm^2

  3. 300π cm^2

  4. 400π cm^2
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The area of a circle is given by the formula πr^2. Substituting r = 10 cm, we get π(10)^2 = 100π cm^2.

Multiple choice

A company wants to produce a rectangular box with a square base and a volume of 1000 cubic centimeters. What dimensions will minimize the surface area of the box?

  1. 10 cm x 10 cm x 10 cm

  2. 12.5 cm x 12.5 cm x 6.67 cm

  3. 15 cm x 15 cm x 4.44 cm

  4. 20 cm x 20 cm x 2.5 cm
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Using calculus, we can find the dimensions that minimize the surface area while satisfying the volume constraint.

Multiple choice

A company wants to design a rectangular box with a square base and a volume of 64 cubic inches. What dimensions will minimize the surface area of the box?

  1. 4 inches x 4 inches x 4 inches

  2. 6 inches x 6 inches x 3.5 inches

  3. 8 inches x 8 inches x 2 inches

  4. 10 inches x 10 inches x 1.6 inches
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Using calculus, we can find the dimensions that minimize the surface area while satisfying the volume constraint.

Multiple choice

What is the value of the area of a circle with a radius of 7 cm?

  1. 154 cm^2

  2. 168 cm^2

  3. 182 cm^2

  4. 196 cm^2
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The area of a circle with a radius of 7 cm is 154 cm^2.

Multiple choice

Calculate the volume of a sphere with radius 10 cm.

  1. 4/3π(1000) cm^3

  2. 4/3π(100) cm^3

  3. 4/3π(10) cm^3

  4. 4/3π cm^3
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

To find the volume of a sphere, use the formula: Volume = (4/3)πr^3. Substitute the radius r = 10 cm: Volume = (4/3)π(10 cm)^3 = 4/3π(1000) cm^3. Therefore, the answer is 4/3π(1000) cm^3.

Multiple choice

A circle has a radius of 5 centimeters. What is the area of the circle?

  1. 25π square centimeters

  2. 50π square centimeters

  3. 75π square centimeters

  4. 100π square centimeters
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The area of a circle is found by using the formula $A = πr^2$. Therefore, the area of the circle is $π imes 5^2 = 25π$ square centimeters.

Multiple choice

A circle has a radius of 10 centimeters. What is the area of the circle?

  1. \(100\pi\) square centimeters
  2. \(200\pi\) square centimeters
  3. \(300\pi\) square centimeters
  4. \(400\pi\) square centimeters
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The area of a circle is given by the formula (A = \pi r^2). Here, the radius (r = 10) centimeters. Plugging this value into the formula, we get: (A = \pi (10)^2 = 100\pi) square centimeters.

Multiple choice

What is the formula for the area of a circle, as given by Bhaskara II?

  1. $\text{Area} = \pi \times \text{radius}^2$
  2. $\text{Area} = 2 \times \pi \times \text{radius}^2$
  3. $\text{Area} = \frac{1}{2} \times \pi \times \text{radius}^2$
  4. $\text{Area} = \frac{1}{4} \times \pi \times \text{radius}^2$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Bhaskara II's formula for the area of a circle is $\text{Area} = \pi \times \text{radius}^2$. This formula is still used today in geometry.

Multiple choice

Find the volume of a sphere with radius (r = 5 cm).

  1. \(100\pi cm^3\)
  2. \(200\pi cm^3\)
  3. \(300\pi cm^3\)
  4. \(400\pi cm^3\)
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

To find the volume of a sphere, we can use the formula: (Volume = \frac{4}{3}\pi r^3). Plugging in the value of (r = 5 cm), we get: (Volume = \frac{4}{3}\pi (5 cm)^3 = \frac{4}{3}\pi (125 cm^3) = 300\pi cm^3).

Multiple choice

What is the area of a rectangle with a length of 10 cm and a width of 5 cm?

  1. 20 cm²

  2. 50 cm²

  3. 100 cm²

  4. 150 cm²
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The area of a rectangle is calculated by multiplying its length and width. In this case, we have 10 cm x 5 cm = 50 cm².