# Grade 7 Surface Area and Volume Worksheet (For CBSE, ICSE, IAS, NET, NRA 2022)

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## (1) Find the Surface Are Of

(a) A cube of side length 8 cm

(b) A cuboid of length 3m, breadth 5m and height 8m.

## (2) Some Identical Cubes of Side Length 5 Cm Are Joined in Different Ways as Shown. Find the Surface Area of the Cube/Cuboid Formed

(a)

(b)

## (3) the Surface Area of a Cube is 150 M^{2}. Find Its Side Length

## (4) the Surface Area of a Cuboid is 492 Cm^{2}. Find the Breadth of the Cuboid if Its Length and Height Are 8 Cm and 12 Cm Respectively

## (5) the Length, Breadth, and Height of a Cuboid Are in the Ratio 4: 3: 5. The Surface Area of the Cuboid is 2350 Cm^{2}. Find Its Length, Breadth, and Height

## (6) a Cuboidal Hall Measures 25m × 12m × 5m. The Walls and Ceiling of the Hall Need to be Plastered. Find the Area to be Plastered

## (7) Rekha Has to Make 80 Cardboard Boxes That Measure 8cm × 9cm × 4cm Each. If the Cardboard Used to Make These Boxes Costs ₹ 5 Per Sq. Cm, How Much Money Would be Required to Buy Cardboard to Make 80 Such Boxes?

## (8) Find the Cost of Painting the Four Walls of a Cuboidal Room of Length 5.2 M, Breadth 3.1 M, and Height 3 M at the Rate of ₹ 40 Per M^{2}

## (9) Find the Cost of Tiling the Floor of a Room Measuring 8m × 6m × 3m at the Rate of ₹ 60 Per M^{2}

## (10) Find the Volume Of

(a) A cube of side length 8cm

(b) A cuboid of dimension 3cm × 8cm × 6cm

## (11) Answer the Following

(a) A surface area of cube is 486 cm^{2} Find its volume

## (12) the Volume of Cuboid of Length 8cm and Breadth 5cm is 80cm^{3} Find Its Surface Area

## (13) Answer the Following

(a) The volume of cube is 343 cm^{3} Find its side length

(b) The volume of cuboid is 120 ft^{3.} Length and height of cuboid is 8ft and 3ft. find the breadth of cuboid.

## (14) Each Side of Cuboid is Increase by 20 % . Find Percentage Increase in the Volume of the Cuboid

## (15) Find the Volume of below Cuboid. Consider Unit of Measurement is Cm

## (16) Find the Volume of below Figure. Consider Unit of Measurement is Cm

## (17) a Solid Bar is in Shape of Cuboid Having Length is 120 Cm, Height 7 Cm and Breadth 5 Cm. If 1cm^{3} Metal Weight is 10g. Find the Weight of the Bar

## (18) a Cubical Water Tank of Side Length 3.4 M

(a) How much water can each tank store?

(b) How much water can 6 such tanks store?

(c) How much water tank required to store 117912 L water? (1m^{3} = 1000L)

## (19) a Metal Bas Measuring 1m X 1.3m X 2.1m is Melted and Recast in to Cuboid Blocks Having Length 20cm Each. How Many Such Blocks Can be Formed?

## (20) Tank Used to Store Chemical is of Cuboid Form of Dimension 12ft X 6ft X 5ft. The Cost of Painting the Tank is ₹ 80 Per Sq. Ft. The Chemical Filled in the Tank Cost ₹ 120 Per Ft^{3.} Find

(a) The cost of painting the tank.

(b) The total worth of chemical in the tank.

## Answers and Explanations

### Answer 1 (A)

- Given that a cube side length
- Now,

- Therefore Surface area of cube is

### Answer 1 (B)

- Given that a cuboid having;
- Length
- Breadth
- Height
- Now,

- Therefore Surface area of cuboid is

### Answer 2 (A)

- Given that side length of identical cube is 5 cm.
- Therefore as shown below figure length (l) of cuboid

- Breadth (b) of cuboid
- Height (h) of cuboid

- Therefore Surface area of cuboid is

### Answer 2 (B)

- Given that side length of identical cube is 5 cm.
- Therefore as shown below figure length (l) of cube

- Breadth (b) of cube
- Height (h) of cube

- Therefore Surface area of cube is

### Answer (3)

- Given that Surface area of cube is
- Suppose side length of cube
- Now

- Therefore Side length of cube is
**5 m**

### Answer (4)

- Given that Surface area of cuboid
- Length (l) of cuboid
- Height (h) of cuboid
- And Breadth of cuboid
- Now for cuboid;

- Therefore breadth of cuboid is
**7.5 cm**

### Answer (5)

- Given that length, breadth, and height of a cuboid are in the ratio 4: 3: 5
- Therefore we can say that length of cuboid
- Breadth of cuboid
- Height of cuboid
- Surface area of cuboid is
- Now for cuboid;

- Therefore Length of cuboid
- Breadth of cuboid
- Height of cuboid

### Answer (6)

- Dimension of cuboid hall is 25m × 12m × 5m
- Therefore length of hall
- Breadth of hall
- And height of hall
- Now plaster to be done on wall and ceiling area only,
- That means all four side wall and ceiling not bottom area
- Therefore Plaster area;

- Therefore plastered area of cuboid shape hall is

### Answer (7)

- Dimension of cardboard boxes is 8cm × 9cm × 4cm
- Means length of cardboard boxes
- Breadth of cardboard boxes
- Height of cardboard boxes
- Now,

- Therefore card board required to make one box
- Rekha has to make 80 cardboard boxes.
- Therefore total cardboard required for this

- Now cost of cardboard is ₹ 5 per sq. cm
- Total cost to make 80 such boxes () is

- Therefore
**₹ 112000**required to buy cardboard to make 80 such boxes.

### Answer (8)

- Length of cuboidal room
- Breadth of cuboidal room
- Height of cuboidal room

- Now,

- Therefore Cost of painting of four wall is
**₹ 1992**

### Answer (9)

- Given that size of room is 8m × 6m × 3m.
- Means length of room
- Breadth of room
- Height of room
- Tiling was done on the floor only; means while calculating tiling area we consider room՚s length and breadth only.
- Therefore

- Now,

- Therefore, cost of tiling the floor of a room is
**₹ 2880**

### Answer 10 (A)

- Given that side length of cube

- Therefore Volume of given cube is

### Answer 10 (B)

- Given that a cuboid having dimension ;
- Length
- Breadth
- Height

- Therefore Volume of given cuboid is

### Answer 11 (A)

- Suppose length of cube is
- Given that surface area of cube is
- We know that,

- Means length of cube
- Now,

- Therefore the volume of cube having surface area is

### Answer (12)

- Given that volume of cuboid is
- Length of cuboid
- Breadth of cuboid
- Suppose height of cuboid

- Therefore height of cuboid
- Now we have for cuboid ,

- Therefore Surface area of cuboid is

### Answer 13 (A)

- Given that volume of cube is
- Suppose side length of cube
- Therefore

- Therefore side length of cube having volume is
**7 cm**

### Answer 13 (B)

- Given that volume of cuboid is
- Length of cuboid
- height of cuboid
- Suppose breadth of cuboid

- Therefore breadth of cuboid

### Answer (14)

- For cuboid suppose;
- Length
- Breadth and
- Height
- Therefore;

- Now if each side of cuboid is increase by 20 % than,

- New length of cuboid
- Same way new breadth of cuboid
- New height of cuboid
- Now

- Therefore

- Now for percentage increase in volume;

- Therefore if each side of cuboid is increase by 20 % than its volume increase by
**72.8 %**

### Answer (15)

- To find the volume of give cuboid, first consider hall cuboid without cavity cuboid.
- Find the volume of hall cuboid than minus volume of cavity cuboid
- For hall cuboid
- Length
- Breadth
- Height
- Now,

Now for cavity cuboid;

- Length
- Breadth
- Height
- Now,

- Now from figure,

- Therefore Volume of given cuboid is

### Answer (16)

- To find the volume of given figure, divide the figure in 3 cuboid as shown in below figure.

- Now for cuboid-1
- Length of cuboid
- Breadth of cuboid
- Height of cuboid
- Now,

- Now for cuboid-2
- Length of cuboid
- Breadth of cuboid
- Height of cuboid
- Now,

- Now for cuboid-3
- Length of cuboid
- Breadth of cuboid
- Height of cuboid
- Now,

- Now,

- Therefore Volume of given figure is

### Answer (17)

- Dimension of solid bar is
- Length
- Breadth
- Height
- Therefore

- Now,

- Therefore weight of the bar is
**42000 g**

### Answer 18 (A)

- Side length of cubical shape water tank is 3.4 m
- Water tank can store water as much its volume.

- Now given than

- Therefore tank can store
**39304 L of water**

### Answer 18 (B)

- One water tank can store 39304L of water.

- Therefore 6 water tank can store 235824 L of water.

### Answer 18 (C)

- One water tank can store 39304 L water.

- Therefore to store 117912 L water 3 water tank required.

### Answer (19)

- Dimension of metal bar
- We know that
- Therefore dimension of metal bar in unit of cm

- Metal bar is melted and recast in to cuboid blocks having length 20cm each
- Therefore

- To find out number of cuboid shape block form from metal bar

- Therefore by melting metal bar
**341 no**of cubical block can formed.

### Answer 20 (A)

- Dimension of cuboid shape tank used to store chemical is
- Therefore length of tank
- Breadth of tank
- Height of tank
- Painting should be done on outside surface area of tank.

- Now for cost evaluation;

- Therefore cost of painting the tank of
**₹ 25920**

### Answer 20 (B)

- Now given that the chemical filled in the tank cost ₹ 120 per ft
^{3} - And tank can store chemical as much its volume and it is
- Now

- Therefore the chemical stored in tank is worth of
**₹ 43200**.