Answer

Verified

381.9k+ views

**Hint:**We are given a bucket in the form of a frustum. We have the upper and lower diameter. We first have to find the radius and then find the curved surface area of the frustum as \[S=\pi \left( R+r \right)l\] where l is the slant height. We can find the slant height (l) using the formula \[l=\sqrt{{{h}^{2}}+{{\left( R-r \right)}^{2}}}\] and then we will find the area and then the total cost by multiplying the area by cost per \[c{{m}^{2}}.\]

__Complete step-by-step answer__:We are given a bucket in the shape of the frustum with the height as 24 cm while the upper circular part that is the diameter is 30 cm while the lower circular part diameter is 10 cm.

So, at first, we will find the radius of the upper and lower circular end and then find the surface area. We are given that the upper diameter is 30cm. Therefore, we know that

\[R=\dfrac{D}{2}\]

Substituting the value of D in the above formula, we get,

\[\Rightarrow R=\dfrac{30}{2}=15cm\]

Therefore, the upper radius, R = 15 cm.

Similarly, the lower diameter is 10 cm. So, we know that

\[r=\dfrac{d}{2}\]

\[\Rightarrow r=\dfrac{10}{2}=5cm\]

Therefore, the lower radius = 5 cm.

So, we have the following details about the frustum.

Height (h) = 24 cm

Upper Circular Radius (R) = 15 cm

Lower Circular Radius (r) = 5 cm

To find the cost of the metal sheet, we have to find the total area of the metal sheet. So,

The total area of the metal sheet = Curved Surface Area of the frustum + Area of the lower circle

\[=\pi \left( r+R \right)l+\pi {{r}^{2}}\]

First, we will find l and then use the above formula. We know that the slant height (l) of the frustum is given as,

\[l=\sqrt{{{h}^{2}}+{{\left( R-r \right)}^{2}}}\]

Here, h = 24, R = 15, r = 5. So,

\[l=\sqrt{{{\left( 24 \right)}^{2}}+{{\left( 15-5 \right)}^{2}}}\]

\[\Rightarrow l=\sqrt{{{24}^{2}}+{{10}^{2}}}\]

\[\Rightarrow l=\sqrt{576+100}\]

\[\Rightarrow l=\sqrt{676}\]

\[\Rightarrow l=\sqrt{{{26}^{2}}}\]

Therefore, we get l = 26 cm.

Now, we have all the required details to find the total area of the metal sheet.

\[\Rightarrow \text{Total Area}=3.14\left( 15+5 \right)26+3.14\times 25\]

\[\Rightarrow \text{Total Area}=3.14\times 20\times 26+3.14\times 25\]

After solving, we will get,

\[\Rightarrow \text{Total Area}=1711.3c{{m}^{2}}\]

Now, we are given that \[100c{{m}^{2}}\] of the metal cost Rs. 10 that means,

\[100c{{m}^{2}}=Rs.10\]

Using the unitary method, we will get,

\[1c{{m}^{2}}=\dfrac{Rs.10}{100}\]

\[1c{{m}^{2}}=\dfrac{Rs.1}{10}\]

Now, we will find the cost of \[1711.3c{{m}^{2}}\] metal sheet.

\[\Rightarrow 1711.3c{{m}^{2}}=\dfrac{1}{10}\times 1711.3\]\[\Rightarrow 1711.3c{{m}^{2}}=Rs.171.13\]

**So, we get the cost of preparing the bucket with the metal sheet as Rs. 171.13.**

**Note**: The curved surface area of the frustum has slant height in its formula. So, students should not take H as l and solve the solution. It will lead to the wrong solution. First students need to find l using the formula \[l=\sqrt{{{h}^{2}}+{{\left( R-r \right)}^{2}}}\] and then use that l to solve the frustum. The conversion of rate into cost per \[c{{m}^{2}}\] is necessary, then only we can find the cost of \[1711.3c{{m}^{2}}\] of the metal.

Recently Updated Pages

Three beakers labelled as A B and C each containing 25 mL of water were taken A small amount of NaOH anhydrous CuSO4 and NaCl were added to the beakers A B and C respectively It was observed that there was an increase in the temperature of the solutions contained in beakers A and B whereas in case of beaker C the temperature of the solution falls Which one of the following statements isarecorrect i In beakers A and B exothermic process has occurred ii In beakers A and B endothermic process has occurred iii In beaker C exothermic process has occurred iv In beaker C endothermic process has occurred

The branch of science which deals with nature and natural class 10 physics CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Define absolute refractive index of a medium

Find out what do the algal bloom and redtides sign class 10 biology CBSE

Prove that the function fleft x right xn is continuous class 12 maths CBSE

Trending doubts

How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Give 10 examples of unisexual and bisexual flowers

What is the color of ferrous sulphate crystals? How does this color change after heating? Name the products formed on strongly heating ferrous sulphate crystals. What type of chemical reaction occurs in this type of change.

Draw a diagram of nephron and explain its structur class 11 biology CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

State the laws of reflection of light

Difference Between Plant Cell and Animal Cell

Change the following sentences into negative and interrogative class 10 english CBSE