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 = 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