# Volume and Surface Area Aptitude Questions With Solutions, Online Test Volume and Surface Area

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Volume and Surface Area online test, mock test, practice sets evaluate aspirants mathematical ability to calculate the Volume and Surface Area of 3D shapes. Aptitude is one of the best topic those are preparing for competitive exams they need to practice on a daily basis to clear the exam. MCQs on volume and surface area are important for securing marks in various competitive exams.

Free online test is good platform to practice Volume and Surface Area questions with solutions.

Learn these tricks and tips to boost your volume and surface area calculations.

## Formulas on Volume and Surface Area

Right Circular Cylinder

Lateral Surface Area: 2πrh

Total Surface Area: 2πr(h+r)

Volume: $πr^2h$ (where r= Radius, h= Height).

Cube

Surface Area: $6a^2$ where a is the dimension of its side.

Volume: $a^3$ where a is the dimension of its side.

Cuboid

Surface Area: 2(lb+ bh+ hl).

Lateral Surface Area: 2(l + b) h (where l= Length, b= Breadth and h= Height)

Volume: l × b × h

Right Circular Cone

Lateral Surface Area: πrl

Total Surface Area: πr(l+r)

Volume: $2/3πr^2h$ (where r= Radius, l=Slant Height and h= Height)

Sphere

Surface Area: $4πr^2$

Volume: $4/3πr^3$ (where r= Radius)

Hemisphere

Curved Surface Area: $2πr^2$

Total Surface Area: $3πr^2$

Volume: $2/3πr^3$ (where r= Radius)

## Questions and Answers on Volume and Surface Area

Question-1)

If a cylinder and a cone have the same height and radius of the base, what is the ratio between the volume of the cylinder and the volume of the cone?

According to the question,

Ratio of their volumes

= ${[πr^2h]} / {[(1/3)πr^2h]}$

= $3/1$

=3 : 1

Question-2)

If a sphere of radius r has the same volume as a cone with a circular base of radius r, what is the height of the cone?

From question,

${\text"Volume of sphere"} = {\text"Volume of cone"}$

⇒ $({4}/{3})πr^3 = ({1}/{3})πr^2h$

⇒ h =4r

Question-3)

A tank is made of the shape of a cylinder with a hemispherical depression at one end. The height of the cylinder is 1.45 m and radius is 30 cm. The total surface area of the tank is?

Total surface area of tank = CSA of cylinder + CSA of hemisphere

= 2πrh + $2πr^2$ = 2πr(h + r)

=$2 × 22/7 × 30(145 + 30) cm^2$

=33000 $cm^2$

= 3.3 $m^2$

Question-4)

The radius of the top and bottom of a bucket of slant height 35 cm are 25 cm and 8 cm. The curved surface of the bucket is?

Curved surface of bucket = $π(r_1 + r_2)$ × slant height (l)

Curved Surface = $(22/7) × (25 + 8) × 35$

CSA = 22 × 33 × 5 = 3630 sq.cm.

Question-5)

The radius of the top and bottom of a bucket of slant height 35 cm are 25 cm and 8 cm. The curved surface of the bucket is?

According to question,

Surface area = $6a^2$ =726

⇒ $a^2$=121

⇒ a = 11 cm

Then, Volume of the cube = (11×11×11)$cm^3$

= $1331cm^3$

 Online Test - 1 (Volume and Surface Area) TAKE TEST Number of questions : 20  |  Time : 30 minutes
 Online Test - 2 (Volume and Surface Area) TAKE TEST Number of questions : 20  |  Time : 30 minutes
 Online Test - 3 (Volume and Surface Area) TAKE TEST Number of questions : 20  |  Time : 30 minutes
 Online Test - 4 (Volume and Surface Area) TAKE TEST Number of questions : 20  |  Time : 30 minutes