Mathematics Volume and Surface Area
Mathematics
Volume of Solids
Formulae for Volume of Solids Cube | Cuboid | Triangular Prism | Cylinder | Cone | Pyramid | Sphere | AnyPrism | s3 | lwh | ½bhl | Πr2h | 1/3πr2h | 1/3Ah | 4/3πr3 | Ah |
A = area of the base of the figure s = length of a side of the figure l = length of the figure w = width of the figure h = height of the figure π = 22/7 or 3.14
1. Compute the volume of a cube with side 7cm.
Volume of cube: s3 s = 7cm s3 = (7cm x 7cm x 7cm) = 343cm3
2. Compute the volume of a cuboid (also known as a rectangular prism) with the dimensions 4cm by 13cm by 9cm.
Volume of a cuboid: lwh l = 4cm w = 13cm h = 9cm lwh = (4cm x 13cm x 9cm) = 468cm3
3. Compute the volume of a triangular prism with a base length of 60cm, a base width of 8cm, and a height of 10cm.
Volume of a triangular prism: ½bhl
½b = (8cm x 1/2) = 4cm h = 10cm l = 60cm
½bhl = (4cm x 10cm x 60cm) = 2400cm3
4. Compute the volume of a cylinder which is 2m tall and has a radius 75cm. Convert this litres.
Volume of a cylinder: πr2h π = 3.1415 r2 = (75cm)2 = 375 cm2 h = 2m = 200cm πr2h = 235612. 5 cm3 cm L = 1cm 0.001 L
235612.5 cm3/ 1000 = 235.6125 L
5. Compute the volume of a cone with a radius of 200cm and a height of 0.75m.
Volume of a cone: 1/3πr2h
1/3π = 1.047 r2 = (2m)2 = 4m2 h = 0.75m
1/3πr2h = (1.047 x 0.75m x 4m2) = 3.141 m3
6. Compute the volume of pyramid with a base length of 10cm, base width 10cm, and the height 18cm.
Volume of a pyramid: 1/3Ah
1/3A = 1/3[(10cm x 10cm) 100cm2] = 33.33 cm2 h = 18cm
1/3Ah = (33.33cm2 x 18cm) = 599.94 cm3
7. Compute the volume of a sphere with a radius of 18cm.
Volume of a sphere: 4/3πr3
4/3π = 4.189 r3 = (18cm)3 = 5832cm3
4/3πr3 = 24430.248cm3
8. A block of wood in the form of a cube has sides of 8cm. A two centimeter wide hole is drilled through the wooden block. Calculate the volume of the wood that remains.
Volume of a cube: s3
Volume of a cylinder: πr2h s3 = (8cm)3 =
Volume of Solids
Formulae for Volume of Solids Cube | Cuboid | Triangular Prism | Cylinder | Cone | Pyramid | Sphere | AnyPrism | s3 | lwh | ½bhl | Πr2h | 1/3πr2h | 1/3Ah | 4/3πr3 | Ah |
A = area of the base of the figure s = length of a side of the figure l = length of the figure w = width of the figure h = height of the figure π = 22/7 or 3.14
1. Compute the volume of a cube with side 7cm.
Volume of cube: s3 s = 7cm s3 = (7cm x 7cm x 7cm) = 343cm3
2. Compute the volume of a cuboid (also known as a rectangular prism) with the dimensions 4cm by 13cm by 9cm.
Volume of a cuboid: lwh l = 4cm w = 13cm h = 9cm lwh = (4cm x 13cm x 9cm) = 468cm3
3. Compute the volume of a triangular prism with a base length of 60cm, a base width of 8cm, and a height of 10cm.
Volume of a triangular prism: ½bhl
½b = (8cm x 1/2) = 4cm h = 10cm l = 60cm
½bhl = (4cm x 10cm x 60cm) = 2400cm3
4. Compute the volume of a cylinder which is 2m tall and has a radius 75cm. Convert this litres.
Volume of a cylinder: πr2h π = 3.1415 r2 = (75cm)2 = 375 cm2 h = 2m = 200cm πr2h = 235612. 5 cm3 cm L = 1cm 0.001 L
235612.5 cm3/ 1000 = 235.6125 L
5. Compute the volume of a cone with a radius of 200cm and a height of 0.75m.
Volume of a cone: 1/3πr2h
1/3π = 1.047 r2 = (2m)2 = 4m2 h = 0.75m
1/3πr2h = (1.047 x 0.75m x 4m2) = 3.141 m3
6. Compute the volume of pyramid with a base length of 10cm, base width 10cm, and the height 18cm.
Volume of a pyramid: 1/3Ah
1/3A = 1/3[(10cm x 10cm) 100cm2] = 33.33 cm2 h = 18cm
1/3Ah = (33.33cm2 x 18cm) = 599.94 cm3
7. Compute the volume of a sphere with a radius of 18cm.
Volume of a sphere: 4/3πr3
4/3π = 4.189 r3 = (18cm)3 = 5832cm3
4/3πr3 = 24430.248cm3
8. A block of wood in the form of a cube has sides of 8cm. A two centimeter wide hole is drilled through the wooden block. Calculate the volume of the wood that remains.
Volume of a cube: s3
Volume of a cylinder: πr2h s3 = (8cm)3 =