Question

$\large {\dag \; {\underline{\underline{\red{\pmb{\sf{ \; Questions \; :- }}}}}}}$


1.] The slant height and base diameter of a conical tomb are 25 m and 14 m respectively. Find the cost of white-washing its curved surface at the rate of 210 per 100 m² .

2.] A joker's cap is in the form of a right circular cone of base radius 7 cm and height 24 cm. Find the area of the sheet required to make 10 such caps.


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Answer 1

Answer:

$\color{darkcyan} \underline{ \begin{array}{ || |l| || } \hline \color{magenta} \\ \hline \boxed{ \text{ \tt \: Solution:-} } \end{array}}$

Step-by-step explanation:

Sol.

$\color{darkviolet} \pmb{\[ \begin{aligned} \text { Base diameter } & \tt=14 m \\ \\ \text { Radius } & \tt=14 m \div 2=7 m \\ \\ \text { Curved surface area } & \tt=\pi l \\ \\ & \tt=\frac{22}{7} \times 7 \times 25 m ^{2}=550 m ^{2} \end{aligned} \]}$

$\red{ \pmb{ \text{Rate of white-washing is \( ₹ 210 \) per \( 100 m ^{2} \)}}}$

Hence cost of white-washing the conical tomb

$\pink{ \tt=₹\left(550 \times \dfrac{210}{100}\right)=₹ 1155 }$

Answer 2

$1. \: \: ➻\:{\underline{\underline\mathfrak\red{Question:--}}}$

The slant height and base diameter of a conical tomb are 25 m and 14 m respectively. Find the cost of white-washing its curved surface at the rate of 210 per 100 m² .

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$➻\:{\underline{\underline\mathfrak\red{Answer:--}}}$

$❑ {\underline{\boxed{\bf\green{Given:}}}}$

Slant height, l = 25 m

Diameter, d = 14 m

curved surface at the rate of 210 per 100 m² .

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$❑ {\underline{\boxed{\bf\green{To \: \: Find:}}}}$

the cost of white-washing the conical tomb = ?

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$❑ {\underline{\boxed{\bf\green{Solution:}}}}$

The slant height of the conical tomb is 25 m and the base diameter is 14 m.

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The curved surface area of a right circular cone of base radius(r) and slant height(l) is πrl

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Slant height, l = √r2 + h2, where h is the height of the cone.

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Diameter, d = 14 m

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$\bf{Radius, r = \frac{14}{2} \: m = 7 \: m}$

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Slant height, l = 25 m

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${\boxed{\bf\pink{Curved \: \: surface \: \: area = πrl}}}$

$\bf= { \frac{22}{7} × 7 m × 25 m}$

$\bf{= {550 \: m}^{2} }$

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Cost of the whitewashing at ₹ 210 per 100 m².

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$\bf{= ( \frac{210}{100} ) × 550}$

$➩{\boxed{\bf\purple{ \: ₹ \: \: 1155}}}$

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➼ Thus, the cost of whitewashing the conical tomb is ₹1155.

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$2. \: \: ➻\:{\underline{\underline\mathfrak\red{Question:--}}}$

A joker's cap is in the form of a right circular cone of base radius 7 cm and height 24 cm. Find the area of the sheet required to make 10 such caps.

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$➻\:{\underline{\underline\mathfrak\red{Answer:--}}}$

$❑{\underline{\boxed{\bf\green{Given:}}}}$

radius, r =7 cm

height, h =24 cm

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$❑ {\underline{\boxed{\bf\green{To \: \: Find:}}}}$

The area of the sheet required to make 10 such caps = ?

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$❑{\underline{\boxed{\bf\green{Solution:}}}}$

Since the cap is conical in shape, the area of the sheet required to make each cap will be equal to the curved surface area of the cone.

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The curved surface area of a right circular cone of base radius(r) and slant height(l) is πrl

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Slant height, l = √r² + h² where h is the height of the cone.

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Radius, r = 7 cm & Height, h = 24 cm

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Slant height,

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${\boxed{\bf\pink{l = √r² + h²}}}$

= √(7)² + (24)²

= √49 + 576

= √625

= 25 cm

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Area of the sheet required to make each cap = πrl

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$\bf= \frac{22}{7} × 7 \: cm × 25 \: cm$

= 550 cm²

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Area of the sheet required to make 10 such caps = 10 × 550 cm²

$➢ \: {\boxed{\bf\purple{ 5500 \: cm²}}}$

➼ Thus, the area of the sheet required to make 10 such caps is 5500 cm2.

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