Mathematics, 23.06.2019 16:00 Almonte87

Asculpture is formed from a cylinder resting on top of a cuboid. the cylinder has a radius 40cm and height 70cm. the cuboid measures 80cm by 80cm by 140cm . the sculpture is made from steel , the steel has a density of 8.05g/cm*3 . calculate the total mass of the sculpture in tonnes. show all working (hurry need to submit assignment asap)

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Answer from: markfaerman5408

Total mass of the sculpture is 11.07 tons .

Step-by-step explanation:

Formula

$Volume\ of\ a\ cylinder = \pi r^{2} h$

Where r is the radius and h is the height .

Volume of a cuboid = Length × Breadth × Height

As given

A sculpture is formed from a cylinder resting on top of a cuboid.

The cylinder has a radius 40cm and height 70cm. the cuboid measures 80cm by 80cm by 140cm .

$\pi = 3.14$

Total volume = Volume of a cylinder + Volume of a cuboid

$Total\ volume = 3.14\times 40\times 40\times 70 + 80\times 80\times 140$

Total volume = 351680 + 896000

= 1247680 cm³

Formula

$Density = \frac{Mass}{Volume}$

As given

The sculpture is made from steel , the steel has a density of 8.05g /cm³ .

$8.05 = \frac{Mass}{1247680}$

Mass = 8.05 × 1247680

= 10043824 g

As 1 tons = 907185 grams

$1\ grams = \frac{1}{907185}\ tons$

Convert 10043824g into tons .

$10043824\ grams = \frac{10043824}{907185}\ tons$

= 11.07 tons

Therefore the total mass of the sculpture is 11.07 tons .

Answer from: Quest

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Answer from: Quest

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1