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Mathematics

1 answer:

sashaice [31]3 years ago

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Please help me I really need help i beg of u due today

nasty-shy [4]

Answer:

The volume of the observatory is 497.43 $feet^{3}$

Step-by-step explanation:

i) The diameter of the floor is 10 feet. The floor is circular and has a radius,

r = $\frac{10}{2}$ = 5 feet.

Therefore the area of the circular floor of the observatory

= $\pi r^{2}$ = 3.14159 × $5^{2}$ = 78.54 $feet^{2}$

ii) The observatory is made up of two parts

a) 3 foot tall cylinder

∴ volume of cylinder = $\pi r^{2}$ × h

= 78.54 × 3

= 235.62 $feet^{3}$

b) hemisphere = $\frac{1}{2}$ × $\frac{4}{3} \pi r^{3}$ = 0.6667 × 78.54 × 5 = 261.81 $feet^{3}$

c) Therefore the total volume of the observatory is = a) + b)

= 235.62 + 261.81 = 497.43 $feet^{3}$

5 0

3 years ago

Laney builds a tower with wooden cubes. The bottom cube's edges are 8 centimeters long. The middle cube's edges are 2 centimeter

Mazyrski [523]

Answer: The total volume of the the cubes in the tower is 792 cubic centimetres (792 cm³)

Step-by-step explanation: We shall call the volume of the cube at the bottom VB, the volume of the cube at the middle VM, and the volume of the cube at the top VT. The tower is made up of cubes at different levels and at the bottom the cube measures 8 centimetres. The cube at the middle measures 2 cm less than the bottom cube, hence middle cube equals 8 minus 2 which equals 6 cm. The top cube measures 2 cm less than the middle cube, hence the top cube equals 6 minus 2 which equals 4 cm. The volume of each cube is given as;

Volume = L³

The length of a cube measures the same on all sides, that is, length, width and height. The length on all sides therefore of the bottom cube is 8 cm. The volume equals;

VB = 8³

VB = 512 cm³

The length on all sides of the middle cube is 6 cm (measures 2 cm shorter than the bottom cube). The volume of the middle cube equals;

VM = L³

VM = 6³

VM = 216 cm³

The length on all sides of the top cube is 4 cm (measures 2 cm shorter than the middle cube). The volume of the top cube equals;

VT = L³

VT = 4³

VT = 64

From the calculations shown, the total volume of the cubes in the tower is given as;

Total volume = VB + VM + VT