Mensuration (Area and Volume): Aptitude Questions – Free Practice!

Ans: C) 200 cm²

Let the breadth be bbb and the length be 2b
Perimeter = 2(l+b)=60
2(2b+b)=60
6b=60
b=10 , l=20
Area = $l \times b = 20 \times 10 = 200$ cm².

Ans: B) 98 cm²

The diagonal of the square equals the diameter of the circle, 2r=14 cm.
Diagonal of the square = $\sqrt{2} \times \text{side}$,
Side = $\frac{\text{diagonal}}{\sqrt{2}} = \frac{14}{\sqrt{2}} = 7\sqrt{2}$
Area = $\text{side}^2 = (7\sqrt{2})^2 = 98$ cm².

Ans: A) $25\sqrt{3}$​ cm²

Area of an equilateral triangle = $\frac{\sqrt{3}}{4} \times \text{side}^2$
Area = $\frac{\sqrt{3}}{4} \times 10^2 = \frac{\sqrt{3}}{4} \times 100 = 25\sqrt{3}$​ cm².

Ans: A) 9 cm

Area of the triangle = $\frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 12 \times 9 = 54$ cm².
Area of the rectangle = $\text{length} \times \text{breadth}$
$6 \times \text{breadth} = 54$
$\frac{54}{6} = 9$ cm.

Ans: C) 748 cm²

Total Surface Area = $2\pi r(h + r)$
=$2 \times \frac{22}{7} \times 7 \times (10 + 7) = 2 \times 22 \times 17 = 748$ cm².

Ans: B) 2688 cm³

Volume of hemisphere = $(2/3) \pi (R^3 – r^3)$ , where R=10, r=8:

V=$\frac{2}{3} \pi (10^3 – 8^3) = \frac{2}{3} \cdot \frac{22}{7} (1000 – 512) = 2688 \, \text{cm}^3$

Ans: B) 5 cm

Slant height = $\sqrt{\text{radius}^2 + \text{height}^2} = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = 5$ cm.

Ans: B) 7 cm

Volume of a sphere = $\frac{4}{3}\pi r^3$
$\frac{4}{3} \times 3.14 \times r^3 = 904.78$
$r^3 = \frac{904.78 \times 3}{4 \times 3.14} = 7^3$
r=7 cm.

Ans: A) 4:5

The ratio of the sides of similar triangles is the square root of the ratio of their areas.
$\sqrt{\frac{16}{25}} = \frac{4}{5}$

Ans: B) 14 cm

Area of semicircle = $\frac{1}{2}\pi r^2$
$\frac{1}{2} \times 3.14 \times r^2 = 154$
$r^2 = \frac{154 \times 2}{3.14} = 98$
$r = \sqrt{98} = 7 cm
Diameter = $2 \times r = 14$ cm.

Ans: A) 54

If the cube’s edge is divided into 3 equal parts, the number of smaller cubes is $3^3 = 27$. The smaller cubes with exactly one face painted are those in the center of each face. Each face has $1^2 = 1$ such cube. Since there are 6 faces: $6 \times 1 = 6$

Ans: B) 539 m³

Volume of a cylinder = $\pi r^2 h$, where $\frac{\text{diameter}}{2} = 3.5$ m and h=14 m.

V= $\pi \times (3.5)^2 \times 14 = \frac{22}{7} \times 12.25 \times 14 = 539 \, \text{m}^3$

Ans: D) 260 cm²

Total Surface Area of a cone = $\pi r (r + l)$, where r=5 cm and l=13 cm.

$\text{TSA} = \pi \times 5 \times (5 + 13) = \frac{22}{7} \times 5 \times 18 = 282.86 \, \text{cm}^2$

Ans: A) 300 cm²

Using Pythagoras theorem, $\text{Diagonal}^2 = \text{Length}^2 + \text{Breadth}^2$ :

$25^2 = 15^2 + \text{Breadth}^2 \implies \text{Breadth} = 20 \, \text{cm}$

Area = $15 \times 20 = 300 \, \text{cm}^2$

Ans: A) 452.16 cm²

Surface Area of a sphere = $\pi r^2$, where $r = \frac{\text{diameter}}{2} = 6$ cm.

$\text{Surface Area} = 4 \times \pi \times 6^2 = 4 \times \frac{22}{7} \times 36 = 452.16 \, \text{cm}^2$

Ans: B) 12 cm

Area of an equilateral triangle = $(\sqrt{3}/4) a^2$. Let side length be a :

$36\sqrt{3} = (\sqrt{3}/4) a^2 \implies a^2 = 144 \implies a = 12 \, \text{cm}$

Ans: B) 10 cm

Volume of water = Volume of cylinder = $\pi r^2 h = \frac{22}{7} \times 7^2 \times 10 = 1540 \, \text{cm}^3$
Height in cuboid = Volume/Base Area = $1540 / 154 = 10 \, \text{cm}$

Ans: A) 12

A regular octahedron has 8 triangular faces, 6 vertices, and 12 edges.

Ans: A) 48 m³

Let dimensions be x,2x,3x. Total surface area:

$2(x \cdot 2x + 2x \cdot 3x + 3x \cdot x) = 88 \implies x^2 = 4 \implies x = 2$

Volume = $x \cdot 2x \cdot 3x = 2 \cdot 4 \cdot 6 = 48 \, \text{m}^3$