Quantitative Aptitude
Mensuration of Solid Figures
147 Questions
Mensuration of solid figures deals with calculating the volume and surface area of 3D shapes. Common structures include cubes, cuboids, and rectangular prisms. These quantitative aptitude questions are standard in SSC, banking, and railway recruitment tests.
Cube volume formulasCuboid surface areaRectangular prismsDensity calculationsDimensional ratios
Mensuration of Solid Figures Questions
What is the formula for the volume of a cube?
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$V = s^3$
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$V = 2s^3$
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$V = 3s^3$
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$V = 4s^3$
A
Correct answer
Explanation
The formula for the volume of a cube is $V = s^3$, where s is the length of one side of the cube.
What is the formula for the surface area of a cube?
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$S = 6s^2$
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$S = 4s^2$
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$S = 2s^2$
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$S = 8s^2$
A
Correct answer
Explanation
The formula for the surface area of a cube is $S = 6s^2$, where s is the length of one side of the cube.
What is the formula for the volume of a pyramid?
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$V = \frac{1}{3}Bh$
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$V = \frac{1}{2}Bh$
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$V = Bh$
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$V = 2Bh$
A
Correct answer
Explanation
The formula for the volume of a pyramid is $V = \frac{1}{3}Bh$, where B is the area of the base of the pyramid and h is the height of the pyramid.
What is the formula for the volume of a prism?
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$V = Bh$
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$V = \frac{1}{2}Bh$
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$V = \frac{1}{3}Bh$
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$V = 2Bh$
A
Correct answer
Explanation
The formula for the volume of a prism is $V = Bh$, where B is the area of the base of the prism and h is the height of the prism.
What is the formula for the volume of a regular tetrahedron?
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$V = \frac{1}{6}a^3$
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$V = \frac{1}{3}a^3$
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$V = \frac{1}{2}a^3$
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$V = a^3$
A
Correct answer
Explanation
The formula for the volume of a regular tetrahedron is $V = \frac{1}{6}a^3$, where a is the length of one edge of the tetrahedron.
What is the formula for the surface area of a regular tetrahedron?
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$S = \sqrt{3}a^2$
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$S = 2\sqrt{3}a^2$
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$S = 3\sqrt{3}a^2$
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$S = 4\sqrt{3}a^2$
A
Correct answer
Explanation
The formula for the surface area of a regular tetrahedron is $S = \sqrt{3}a^2$, where a is the length of one edge of the tetrahedron.
What is the formula for the volume of a cube with side length (s)?
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\(s^3\)
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\(s^2\)
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\(2s^3\)
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\(4s^3\)
A
Correct answer
Explanation
The volume of a cube is given by the formula (s^3), where (s) is the length of one side of the cube.
What is the formula for the surface area of a cube with side length (s)?
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\(6s^2\)
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\(4s^2\)
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\(2s^2\)
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\(s^2\)
A
Correct answer
Explanation
The surface area of a cube is given by the formula (6s^2), where (s) is the length of one side of the cube.
What is the formula for the volume of a rectangular prism with length (l), width (w), and height (h)?
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\(lwh\)
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\(2lwh\)
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\(lw\)
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\(l^2w^2h^2\)
A
Correct answer
Explanation
The volume of a rectangular prism is given by the formula (lwh), where (l) is the length, (w) is the width, and (h) is the height of the prism.
What is the formula for the volume of a pyramid with base area (B) and height (h)?
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\(\frac{1}{3}Bh\)
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\(\frac{1}{2}Bh\)
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\(Bh\)
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\(2Bh\)
A
Correct answer
Explanation
The volume of a pyramid is given by the formula (\frac{1}{3}Bh), where (B) is the area of the base and (h) is the height of the pyramid.
What is the formula for the volume of a triangular prism with base area (B) and height (h)?
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\(\frac{1}{2}Bh\)
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\(Bh\)
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\(2Bh\)
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\(3Bh\)
A
Correct answer
Explanation
The volume of a triangular prism is given by the formula (\frac{1}{2}Bh), where (B) is the area of the base and (h) is the height of the prism.
What is the volume of a cube with a side length of 5 centimeters?
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25 cubic centimeters
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50 cubic centimeters
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125 cubic centimeters
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250 cubic centimeters
C
Correct answer
Explanation
The volume of a cube is calculated by cubing its side length. Therefore, the volume of the cube with a side length of 5 centimeters is (5^3 = 125) cubic centimeters.
What is the formula for the volume of a rectangular prism, as given by Bhaskara II?
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$\text{Volume} = \text{length} \times \text{width} \times \text{height}$
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$\text{Volume} = 2 \times \text{length} \times \text{width} \times \text{height}$
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$\text{Volume} = \frac{1}{2} \times \text{length} \times \text{width} \times \text{height}$
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$\text{Volume} = \frac{1}{4} \times \text{length} \times \text{width} \times \text{height}$
A
Correct answer
Explanation
Bhaskara II's formula for the volume of a rectangular prism is $\text{Volume} = \text{length} \times \text{width} \times \text{height}$. This formula is still used today in geometry.
What is the formula for the volume of a pyramid, as given by Bhaskara II?
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$\text{Volume} = \frac{1}{3} \times \text{base area} \times \text{height}$
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$\text{Volume} = \frac{1}{2} \times \text{base area} \times \text{height}$
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$\text{Volume} = \frac{2}{3} \times \text{base area} \times \text{height}$
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$\text{Volume} = \frac{3}{4} \times \text{base area} \times \text{height}$
A
Correct answer
Explanation
Bhaskara II's formula for the volume of a pyramid is $\text{Volume} = \frac{1}{3} \times \text{base area} \times \text{height}$. This formula is still used today in geometry.
What is the volume of a cube with a side length of 4 cm?
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16 cm³
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32 cm³
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64 cm³
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128 cm³
C
Correct answer
Explanation
The volume of a cube is calculated by cubing its side length. In this case, we have 4 cm x 4 cm x 4 cm = 64 cm³.