Mathematics, 23.01.2020 22:31 barnettboy76

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Answer from: roselyn3301

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 $feet^{3}$

Answer from: Quest

circle area = pi * radius^2

if diameter = 10 then radius = 5

circle area = pi * 5^2

circle area = pi * 25

circle area = 78.5398163397 square units

step-by-step explanation:

Answer from: Quest

Answer: question no. 1 -a. yes, the sides are in the ratio 2 : 5.question no. 2 -b. 59°question no. 3 -c. angles x and y are remote interior angles.question no. 4 -d. 90°, 45° and 45°question no. 5 -b. mn and qrstep-by-step explanation: question no. 1 -rs : xu = 3 : 7.5 = 2 : 5rt : x? = 6.4 : 16 = 2 : 5st : u? = 6 : 15 = 2 : 5as the ratios of all sides are equivalent, the triangles must be congruent and the sides must be proportional.therefore, the answer is: a. yes, the sides are in the ratio 2 : 5.question no. 2 -in the second diagram, angle b is the only letter not shown. therefore, the number must be equivalent to angle b.if we substitute the value of angle b as being 22° in the first diagram, we can now use the angle sum of a triangle to obtain the value of angle a.angle sum of a triangle = 180°therefore: let angle a = aa + 99 + 22 = 180a = 180 - 99 - 22a = 59°therefore, the answer is: b. 59°question no. 3 -angles x and y don't share the vertex of the triangle with the exterior angle w. remote interior angles don't share a vertex of a triangle with an exterior angle. this means that angles x and y are remote interior angles.therefore, the answer is: c. angles x and y are remote interior angles.question no. 4 -the sum of all interior angles of a triangle must be equivalent to 180°.90°, 45° and 45° are the only set of angle measures that are equivalent to 180°.therefore, the answer is: d. 90°, 45° and 45°question no. 5 -the only pair of sides stated in the options which are corresponding are mn and qr.therefore, the answer is: b. mn and qr.

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