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3 years ago

Kindly i need solution of these both parts a and b which are attached below

Mathematics

1 answer:

Nikitich [7]3 years ago

3 0

9514 1404 393

Answer:

a) 252 cm³, 252 cm², 705.6 g

b) 240 cm³, 252 cm², 672 g

Step-by-step explanation:

The volume of each figure can be computed as the product of the base area (the side facing the viewer) and the "height" of the prism (the distance between bases).

The surface area of the prism is the sum of the two base areas and the "lateral area" consisting of the product of the base perimeter and the "height" of the prism.

The mass will be the product of volume and density.

ai) The base is a 3 cm by 8 cm rectangle together with a trapezoid with bases 3 cm and 6 cm, and height 7 - 3 = 4 cm.

B = (3 cm)(8 cm) +(1/2)(3 cm +6 cm)(4 cm) = 24 cm² +18 cm² = 42 cm²

The "height" is 6 cm, so the volume is ...

V = Bh = (42 cm²)(6 cm) = 252 cm³

aii) The perimeter of the base is the sum of its side lengths. Clockwise from left, the lengths are ...

(8 +3 +2 +5 +3 +7) cm = 28 cm

Then the lateral area is ...

LA = Ph = (28 cm)(6 cm) = 168 cm²

Adding this to the areas of the two bases, we get the total surface area:

A = LA +2B = (168 cm²) + 2(42 cm²) = 252 cm²

aiii) The mass is the product of volume and density:

M = ρV = (2.8 g/cm³)(252 cm³) = 705.6 g

____

bi) This trapezoidal prism has a base that has bases of 6 and 9 cm, and a height of 4 cm. The area of the base is ...

B = (1/2)(b1 +b2)h = (1/2)(6 cm + 9cm)(4 cm) = 30 cm²

Then the volume is ...

V = Bh = (30 cm²)(8 cm) = 240 cm³

bii) The lateral area is the perimeter of the base times the height of the prism:

LA = Ph = (4 +6 +5 +9 cm)(8 cm) = 192 cm²

The total area is this area plus that of the two bases:

A = LA +2B = (192 cm²) +2(30 cm²) = 252 cm²

biii) M = ρV = (2.8 g/cm³)(240 cm³) = 672 g

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Answer:

Step-by-step explanation:

From the problem statement, we can set up the following two equations:

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We can substitute the first equation into the second and solve for $K$

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An oil tank has to be drained for maintenance. The tank is shaped like a cylinder that is 3ft long with a diameter of 2.2 ft . S

Contact [7]

4 minutes 34 seconds will takes to empty the tank, if the starts completely full and oil drained at a rate of 2.5 $ft^{3}$ per minute.

Step-by-step explanation:

The given is,

Tank is shaped like a cylinder that is 3 ft long with a diameter of 2.2 ft.

Oil drained at a rate of 2.5 $ft^{3}$ per minute.

Step:1

Time taken to dry the oil tank is,

T = $\frac{Volume of oil}{Oil drain rate}$ ....................................(1)

Step:2

Volume of the oil is,

$V = \pi r^{2} h$ .................................................(2)

Where, r - Radius of Cylinder

$r = \frac{d}{2}$

$r = \frac{2.2}{2}$

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From eqn (1),

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Step:3

From equation (1)

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= 4.56 minutes

T = 4 minutes 34 seconds

Result:

Time taken to dry the oil tank is 4 minutes 34 seconds, if a cylinder is 3 ft long with a diameter of 2.2 ft and oil is drained at a rate of 2.5ft^3 per minute.

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