### Quantitative Aptitude

## VOLUME AND SURFACE AREA MCQs

### Total Questions : 189

**Page 1 of 10 pages**

**A hollow spherical metallic ball has an external diameter 6 cm and is $$\frac{1}{2}$$ cm thick. The volume of metal used in the ball is :**

__Question 1.__- $$37\frac{2}{3}{\text{ c}}{{\text{m}}^3}$$
- $$40\frac{2}{3}{\text{ c}}{{\text{m}}^3}$$
- $$41\frac{2}{3}{\text{ c}}{{\text{m}}^3}$$
- $$47\frac{2}{3}{\text{ c}}{{\text{m}}^3}$$

**Answer: Option D**

**V1, V2, V3 and V4 are the volumes of four cubes of side lengths x cm, 2x cm, 3x cm and 4 cm respectively. Some statements regarding these volumes are given below :**

__Question 10.__(i) V1 + V2 + 2V3 < V4

(ii) V1 + 4V2 + V3 < V4

(iii) 2(V1 + V3) + V2 = V4

Which of these statements area correct ?

- 1 and 2
- 2 and 3
- 1 and 3
- 1, 2 and 3

**Answer: Option D**

### Do Volume And Surface Area Increase Proportionally?

Surface Area to Volume Ratio -

The ratio between the surface area and volume will determine the speed of material exchange, calculated by dividing the surface area by the volume. The surface area and volume will not increase proportionally as the object increases in size.

### How Do You Find Surface Area With Volume?

The volume of a solid is the amount the shape contains. Volume is a measure of capacity and is measure in cubic units. To calculate the volume of a rectangular prism, multiply the area of the base (length Ã— width) times height.

### How Do You Find Surface Area?

The total surface area is calculated by adding all the areas on the surface: the areas of the base, top, and lateral surfaces (sides) of the object. This is done using different area formulas and measured in square units. Volume is the amount of space that a three dimensional object takes up.

### Is Surface Area And Total Surface Area The Same?

The surface area of a floor is everything you can walk on. So, the surface area of a rectangle, circle, triangle, or other shape is simply a measurement of everything within the lines of the shape. For a two-dimensional object, that's also its total surface area.

### Is Surface Area Directly Proportional To Volume?

As a result, the surface area to volume ratio is inversely proportional to the size of an object, given that length and radius determine the size.

### What Are The Types Of Surface Areas?

There are three types of surface area: lateral surface area, curved surface area, and total surface area.

### What Is The Difference Between Surface Area And Total Surface Area?

The lateral surface of an object is the area of all the faces of the object, excluding the area of its base and top. For a cube, the lateral surface area would be the area of four sides. Total surface area is the area of all the faces including the bases.

### What Is The Surface Area Of The Solid?

The total surface area of a solid is the sum of the areas of all of the faces or surfaces that enclose the solid. The faces include the tops and bottoms (bases) and the remaining surfaces. The lateral surface area of a solid is the surface area of the solid without the bases.

### What Is Volume?

In mathematics, 'Volume' is a mathematical quantity that shows the amount of three-dimensional space occupied by an object or a closed surface.

### Are Surface Area And Volume Directly Proportional?

One interesting thing that you should notice is that the surface area to volume ratio is inversely proportional to the size of an object.

### How Are Surface And Volume Related?

As you can see from the formulas, surface area is square function (side 2 x 6), while volume is a cubic function (side)3. As a result, as the size of an object increases, its ratio of surface area to volume decreases. Conversely, as the size of an object decreases, its ratio of surface area to volume increases.

### How Do I Find The Surface Area Of A Square?

For a square you only need to find the length of one of the sides (as each side is the same length) and then multiply this by itself to find the area. This is the same as saying length2 or length squared. It is good practice to check that a shape is actually a square by measuring two sides.

### How Do You Learn Surface Area And Volume In Math?

Surface area and volume are calculated for any three-dimensional geometrical shape. The surface area of any given object is the area or region occupied by the surface of the object.

Surface Area Of A Cone | Volume of a Cone |
---|---|

Surface Area Of Cube | Volume Of A Cube |

Surface Area of Cuboid | Volume Of Cuboid |

### How Does Volume Affect Surface Area?

As volume and surface area increase, the volume increases faster, so much so that the surface area available to allow substances in halves each time the cell volume doubles. This is known as the surface area/volume ratio (SA/V ratio).

### Is Surface Area And Area The Same Thing?

The area is the measurement of the size of flat-surface in a plane (two-dimensional), whereas surface area is the measurement of the exposed surface of a solid shape (three-dimensional). This is the key difference between area and surface area. The unit for both the quantities is the same, though, i.e. square units.

### What Is Surface Area Explain?

Surface area is the amount of space covering the outside of a three-dimensional shape.

### What Is The Difference Between Surface Area And Surface Area To Volume Ratio?

Surface area is how much area of the object is exposed to the outside. The volume is how much space is inside the shape. The surface-area-to-volume ratio tells you how much surface area there is per unit of volume. This ratio can be noted as SA:V.

### What Is The Relationship Between Surface Area And Volume?

As you can see from the formulas, surface area is square function (side 2 x 6), while volume is a cubic function (side)3. As a result, as the size of an object increases, its ratio of surface area to volume decreases. Conversely, as the size of an object decreases, its ratio of surface area to volume increases.

### Why Does Volume Increase Faster Than Surface Area?

When the cell increases in size, the volume increases faster than the surface area, because volume is cubed where surface area is squared.

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