Solve the following mathematical problems:

A semi circular sheet of metal of diameter 28 cm is bent into an open conical cup. Find the depth and capacity of cup.

Created: 3 months ago | Updated: 3 months ago

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Radius of semi circular sheet, $r = \frac{28}{2} 14 m$

Circumference of the sheet = $πr = (\frac{22}{7} \times 14) = 44 cm$

Here, circumference of semi circle will be equal to the circumference of the base of cone.

Now, let the radius of the base of cone = R

According to question = $= 2 πR = 44 = R = \frac{44}{2 π} = \frac{44}{\frac{22 \times 2}{7}} = 44 \times \frac{7}{22 \times 2} = 7 cm$

Here, radius of semi circle equals to the height of cone.

That mean's l = r = 14 cm

Now, we know $^{2} = h^{2} + R^{2} \Rightarrow h^{2} = l^{2} - R^{2} \Rightarrow h^{2} = {(14)}^{2} - {(7)}^{2} = 196 - 49 = 147 \Rightarrow h = \sqrt{49 \times 3} = \sqrt{7^{2} \times 3} = 7 \sqrt{3} ∴ h = 7 \sqrt{3}$

So, the depth is $7 \sqrt{3}$ cm and

The capacity will be = $(\frac{1}{3} {πr}^{2} h) = (\frac{1}{3} \times \frac{22}{7} \times 7^{2} \times 7 \sqrt{3}) = 622.37 c m^{3}$ (ans)

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Differentiate financial and economic costs with suitable example. The total revenue (TR) and Average Cost (AC) functions of a firm are given by $T R = 4350 Q - 13 Q^{2} A C = Q^{2} - 5.5 Q + 150 + 675 Q^{2}$ Where Q refers to quantity of output. Find the profit maximizing level of output and maximum profit.

Created: 3 months ago | Updated: 3 months ago

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Suppose C=$35+0.80Yd, I = $70, G= $65, Tx = 0.10Y.

Find the equilibrium output,

Created: 3 months ago | Updated: 3 months ago

Job Solution Bangladesh Bank Bangladesh Bank || Assistant Director (19-04-2019) || 2019 গণিত

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Suppose C=$35+0.80Yd, I = $70, G= $65, Tx = 0.10Y.

What are the tax revenue at equilibrium output? Does the government have a balanced budget?

Created: 3 months ago | Updated: 3 months ago

Job Solution Bangladesh Bank Bangladesh Bank || Assistant Director (19-04-2019) || 2019 গণিত

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Suppose C=$35+0.80Yd, I = $70, G= $65, Tx = 0.10Y.

Find the equilibrium output when investment increases from $70 to $90.

Created: 3 months ago | Updated: 3 months ago

Job Solution Bangladesh Bank Bangladesh Bank || Assistant Director (19-04-2019) || 2019 গণিত

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Suppose C=$35+0.80Yd, I = $70, G= $65, Tx = 0.10Y.

What has happened to the relationship of government spending and tax revenues? Why?

Created: 3 months ago | Updated: 3 months ago

Job Solution Bangladesh Bank Bangladesh Bank || Assistant Director (19-04-2019) || 2019 গণিত

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Solve the following mathematical problems:

A semi circular sheet of metal of diameter 28 cm is bent into an open conical cup. Find the depth and capacity of cup.

Related Questions

Differentiate financial and economic costs with suitable example. The total revenue (TR) and Average Cost (AC) functions of a firm are given by TR=4350Q-13Q2AC=Q2-5.5Q +150+675Q2 Where Q refers to quantity of output. Find the profit maximizing level of output and maximum profit.

Suppose C=$35+0.80Yd, I = $70, G= $65, Tx = 0.10Y.

Find the equilibrium output,

Suppose C=$35+0.80Yd, I = $70, G= $65, Tx = 0.10Y.

What are the tax revenue at equilibrium output? Does the government have a balanced budget?

Suppose C=$35+0.80Yd, I = $70, G= $65, Tx = 0.10Y.

Find the equilibrium output when investment increases from $70 to $90.

Suppose C=$35+0.80Yd, I = $70, G= $65, Tx = 0.10Y.

What has happened to the relationship of government spending and tax revenues? Why?