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)

Illustration 2 for 2_Some_identical_cubes_of_side_ …

(b)

Illustration 3 for 2_Some_identical_cubes_of_side_ …

(3) the Surface Area of a Cube is 150 M2. Find Its Side Length

(4) the Surface Area of a Cuboid is 492 Cm2. 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 Cm2. 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 M2

(9) Find the Cost of Tiling the Floor of a Room Measuring 8m × 6m × 3m at the Rate of ₹ 60 Per M2

(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 cm2 Find its volume

(12) the Volume of Cuboid of Length 8cm and Breadth 5cm is 80cm3 Find Its Surface Area

(13) Answer the Following

(a) The volume of cube is 343 cm3 Find its side length

(b) The volume of cuboid is 120 ft3. 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

Illustration 4 for 15_Find_the_volume_of_below_cub …

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

Illustration 5 for 16_Find_the_volume_of_below_fig …

(17) a Solid Bar is in Shape of Cuboid Having Length is 120 Cm, Height 7 Cm and Breadth 5 Cm. If 1cm3 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? (1m3 = 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 Ft3. 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
Illustration 6 for Answers_and_Explanations

  • 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
Illustration 7 for Answers_and_Explanations

  • 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.
Illustration 8 for Answers_and_Explanations
  • 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 ft3
  • And tank can store chemical as much its volume and it is
  • Now

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

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