# Mathematics Volume and Surface Area

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 = (8cm x 8cm x 8cm) = 512cm3

π = 3.14

r2 = {(2cm)/2}2 = 1cm2

h = 8cm

πr2h = (3.14 x 8cm x 1cm2) = 25.12cm3

Volume of the remaining wood block = Volume of the cube - Volume of the hole 512cm3 – 25.12cm3 = 486.88cm3

9. A netball has a radius of 14cm and when pumped up it forms a sphere. A pump will fill a ball at a rate of 30cm3 of air every time it is pushed. Calculate the number of times the pump must be pushed to fill the ball. Volume of a sphere: 4/3πr3

4/3π = 4.186

r3 = (14cm)3 = (14cm x 14cm x 14cm) = 2744cm3

4/3πr3 = (4.186 x 2744cm3) = 11486.384cm3

11486.384cm3/30cm3 = 382.87 times

10. A cuboid shaped swimming pool is 50m long, 25m wide and 2m deep. The walls of the pool are 50cm thick. Calculate the volume of concrete needed to fill the walls of the pool. Volume of a cuboid: lwh

l = 50m

w = 25m

h = 2m

lwh = (50m x 25m x 2m) = 2500m3

l = 50m – 50cm = 49.5m

w = 25m – 50cm = 24.5m

h = 2m

lwh = (49.5m x 24.5m x 2m) = 2425.5m3

Volume of concrete needed: 2500cm3 – 2425.5cm3 = 74.5cm3

11. Construct the net of a triangular prism with a length of 10cm and equilateral triangles of 5cm for cross-sections.

12. Construct the net of a pyramid with a square base of 10cm and sides which are equilateral triangles.

13. Create a question of your own. Do not download the question from the Internet or copy it from a book. If you do so, you will receive zero points for this question.

Question:

An irregularly shaped cake at a bakery has four tiers. The first tier is a cylinder with a radius of 8cm and a height of 20cm. The second tier is a sphere with a radius of 10cm.The following tier is a cube with a height of 12cm and the final tier is a cone with a radius of 13cm and a height of 15cm. If James goes to the bakery and buys 11 of this cake, what volume of cake does he have?

14. Calculate the surface area of every figure in questions 1 through 7.

Question 1

Surface area of a cube: 6s2

(6 x 7cm2) = 294cm2

Question 2

Surface area of...

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