Contents

**Volume and Surface Area – Maharashtra Board Class 7 Solutions for Mathematics (English Medium)**

MathematicsGeneral ScienceMaharashtra Board Solutions

### Exercise-84

**Solution 1:**

- The measure of the place occupied by an object in space is called its
__volume__. - The standard units of length are
__centimeter__and__metre__. - The standard units of area are
__sq. cm__and__sq. m__. - The cube whose length, breadth and height are each 1 cm has a volume of 1
__cu. cm__. - The cube whose length, breadth and height are each 1 m has a volume of 1
__cu. m__.

### Exercise-85

**Solution 1:**

- Cupboard
- Matchbox
- Cake of soap
- Book
- Trunk

**Solution 2:**

- Each face of a cube is
__square in shape__. - A cuboid has
__12__edges. - A cube has
__6__face altogether. - A cuboid has altogether
__8__vertices. - The standard units of volume are
__cu. cm__and__cu. m__. - All edges of a cube are of
__equal__length.

**Solution 3:**

- Vertices: P, Q, R, S, W, T, U, V
- Edges: seg PQ, seg QR, seg RS, seg SP, seg PW, seg WT, seg TU, seg UV, seg SV, seg RU, seg QT, seg VW
- Face: Square PQRS, square QRTU, square WTVU, square PWSV, square PQWT and square SRVU
- Vertex R is common to seg RQ, seg RS and seg RU.
- Vertex W is common to the seg WT, seg WV and seg WP.
- The edges PW and WT intersect at vertex W.
- Square PQRS is opposite to the square TUVW.

### Exercise-86

**Solution 1:**

- Volume of cube = (l)
^{3}= (26)^{3}= 17576 cu. cm - Volume of cube = (l)
^{3}= (2.6)^{3}= 17.576 cu. cm - Volume of cube = (l)
^{3}= (3.9)^{3}= 59.319 cu. cm - Volume of cube = (l)
^{3}= (12.5)^{3}= 1953.125 cu. cm - Volume of cube = (l)
^{3}= (13.2)^{3}= 2299.968 cu. cm - Volume of cube = (l)
^{3}= (24.3)^{3}= 14348.907 cu. cm - Volume of cube = (l)
^{3}= (9.7)^{3}= 912.673 cu. cm - Volume of cube = (l)
^{3}= (10.3)^{3}= 1092.727 cu.cm

**Solution 2:**

Side of the cube (l) = 2.5 cm.

Volume of the cubic die = Volume of a die = (l)^{3}

= (2.5)^{3}

= 15.625 cu. cm

**Solution 3:**

Side of the cube (l) = 6 m

Volume of water in a cube-shaped tank = Volume of cube = (l)^{3}

= (6)^{3}

= 216 cu. m

Thus, the cube-shaped tank can hold 216 cu. m of water.

**Solution 4:**

Side of the cube-shaped box (l) = 1.9 cm

Volume of the cube-shaped box = (l)^{3}

= (1.9)^{3}

= 6.859 cu. cm

Thus, the volume of the cube-shaped box is 6.859 cu. cm.

### Exercise-87

**Solution 1:**

1. Total surface area of a cube = 6l^{2}

= 6(3)^{2}

= 6 × 3 × 3

= 54 sq. cm

2. Total surface area of a cube = 6l^{2}

= 6(5)^{2}

= 6 × 5 × 5

= 150 sq. cm

3. Total surface area of a cube = 6l^{2}

= 6(7.2)^{2}

= 6 × 7.2 × 7.2

= 311.04 sq. m

4. Total surface area of a cube = 6l^{2}

= 6(6.8)^{2}

= 6 × 6.8 × 6.8

= 277.44 sq. m

5. Total surface area of a cube = 6l^{2}

= 6(9.3)^{2}

= 6 × 9.3 × 9.3

= 518.94 sq. cm

6. Total surface area of a cube = 6l^{2}

= 6(5.8)^{2}

= 6 × 5.8 × 5.8

= 201.84 sq. cm

7. Total surface area of a cube = 6l^{2}

= 6(8.6)^{2}

= 6 × 8.6 × 8.6

= 443.76 sq. cm

**Solution 2:**

Side of the cube (l) = 5.5 cm

Total surface area = 6l^{2}

= 6(5.5)^{2}

= 6 × 5.5 × 5.5

= 181.5 sq. cm

**Solution 3:**

Side of the safe (l) = 0.5 m

Total surface area = 6l^{2}

= 6(0.5)^{2}

= 6 × 0.5 × 0.5

= 1.5 sq. m

Cost of painting 1 sq. m = Rs. 60

∴ Cost of painting 1.5 sq. m = Rs. (60 × 1.5)

= Rs. 90

Thus, the cost to paint all sides of the safe is Rs. 90.

**Solution 4:**

**Solution 5:**

**Solution 6:**

**Solution 7:**

### Exercise-88

**Solution 1:**

1. l = 14 cm, b = 12 cm, h = 8 cm

Volume of a cuboid = l × b × h

= 14 × 12 × 8

= 1344 cu. cm

2. l = 20.5 cm, b = 16 cm, h = 10 cm

Volume of a cuboid = l × b × h

= 20.5 × 16 × 10

= 3280 cu. cm

3. l = 7.5 cm, b = 5.2 cm, h = 4.5 cm

Volume of a cuboid = l × b × h

= 7.5 × 5.2 × 4.5

= 175.5 cu. cm

4. l = 1.4 cm, b = 1.1 cm, h = 0.6 cm

Volume of a cuboid = l × b × h

= 1.4 × 1.1 × 0.6

= 0.924 cu. cm

5. l = 2.2 cm, b = 1.5 cm, h = 0.9 cm

Volume of a cuboid = l × b × h

= 2.2 × 1.5 × 0.9

= 2.97 cu. cm

**Solution 2:**

**Solution 3:**

**Solution 4:**

**Solution 5:**

l = 1.8 km = 1.8 × 1000 = 1800 m, b = 8 m,

h = 15 cm = (15 ÷ 100) m = 0.15 m

Volume of the required metal = l × b × h

= 1800 × 8 × 0.15

= 2160 cu. m

Thus, the required volume of the metal is 2160 cu. m.

**Solution 6:**

l = 7.5 m, b = 2.4 m, h = 3 m

Volume of the tank = l × b × h

= 7.5 × 2.4 × 3

= 54 cu. m

Thus, the tank will hold 54 cu. m of water.

**Solution 7:**

### Exercise-89

**Solution 1:**

l = 1.5 m, b = 1.2 m, h = 1.3 m

Total surface area of the trunk

= 2(l × b + b × h + h × l)

= 2(1.5 × 1.2 + 1.2 × 1.3 + 1.3 × 1.5)

= 2(1.80 + 1.56 + 1.95)

= 2 × 5.31

= 10.62 sq. m

**Solution 2:**

l = 12 cm, b = 10 cm, h = 5 cm

Metal sheet required

= 2(l × b + b × h + h × l)

= 2(12× 10 + 10 × 5 + 5 × 12)

= 2(120 + 50 + 60)

= 2 × 230

= 460 sq. cm

**Solution 3:**

l = 4 cm, b = 2.5 cm, h = 1.5 cm

Paper required = Total surface area of the matchbox

= 2(l × b + b × h + h × l)

= 2(4 × 2.5 + 2.5 × 1.5 + 1.5 × 4)

= 2(10.00 + 3.75 + 6.0)

= 2 × 19.75

= 39.5 sq. cm

**Solution 4:**

l = 2.5 m, b = 2 m, h = 2.4 m

Metal sheet required

= 2(l × b + b × h + h × l)

= 2(2.5 × 2 + 2 × 2.4 + 2.4 × 2.5)

= 2(5 + 4.8 + 6)

= 2 × 15.8

= 31.6 sq. m

Cost of constructing 1 sq. m = Rs. 10

∴ Cost of constructing 31.6 sq. m = Rs. (31.6 × 10)

= Rs. 316

Volume of the tank = l × b × h

= 2.5 × 2 × 2.4

= 12 cu. m