Volume and Surface Area – Maharashtra Board Class 7 Solutions for Mathematics

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

MathematicsGeneral ScienceMaharashtra Board Solutions

Exercise-84

Solution 1:

1. The measure of the place occupied by an object in space is called its volume.
2. The standard units of length are centimeter and metre.
3. The standard units of area are sq. cm and sq. m.
4. The cube whose length, breadth and height are each 1 cm has a volume of 1 cu. cm.
5. The cube whose length, breadth and height are each 1 m has a volume of 1 cu. m.

Exercise-85

Solution 1:

1. Cupboard
2. Matchbox
3. Cake of soap
4. Book
5. Trunk

Solution 2:

1. Each face of a cube is square in shape.
2. A cuboid has 12 edges.
3. A cube has 6 face altogether.
4. A cuboid has altogether 8 vertices.
5. The standard units of volume are cu. cm and cu. m.
6. All edges of a cube are of equal length.

Solution 3:

1. Vertices: P, Q, R, S, W, T, U, V
2. 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
3. Face: Square PQRS, square QRTU, square WTVU, square PWSV, square PQWT and square SRVU
4. Vertex R is common to seg RQ, seg RS and seg RU.
5. Vertex W is common to the seg WT, seg WV and seg WP.
6. The edges PW and WT intersect at vertex W.
7. Square PQRS is opposite to the square TUVW.

Exercise-86

Solution 1:

1. Volume of cube = (l)³ = (26)³ = 17576 cu. cm
2. Volume of cube = (l)³ = (2.6)³ = 17.576 cu. cm
3. Volume of cube = (l)³ = (3.9)³ = 59.319 cu. cm
4. Volume of cube = (l)³ = (12.5)³ = 1953.125 cu. cm
5. Volume of cube = (l)³ = (13.2)³ = 2299.968 cu. cm
6. Volume of cube = (l)³ = (24.3)³ = 14348.907 cu. cm
7. Volume of cube = (l)³ = (9.7)³ = 912.673 cu. cm
8. 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 = 6l²
= 6(3)²
= 6 × 3 × 3
= 54 sq. cm

2. Total surface area of a cube = 6l²
= 6(5)²
= 6 × 5 × 5
= 150 sq. cm

3. Total surface area of a cube = 6l²
= 6(7.2)²
= 6 × 7.2 × 7.2
= 311.04 sq. m

4. Total surface area of a cube = 6l²
= 6(6.8)²
= 6 × 6.8 × 6.8
= 277.44 sq. m

5. Total surface area of a cube = 6l²
= 6(9.3)²
= 6 × 9.3 × 9.3
= 518.94 sq. cm

6. Total surface area of a cube = 6l²
= 6(5.8)²
= 6 × 5.8 × 5.8
= 201.84 sq. cm

7. Total surface area of a cube = 6l²
= 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 = 6l²
= 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 = 6l²
= 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