Answer
Verified
388.8k+ views
Hint: Here we use the concept of volume of frustum. We need to find the capacity of the reservoir which is in the shape of frustum.
$\text{V}olume\text{ }of\text{ }frustrum\text{ }of\text{ }cone=\dfrac{1}{3}\pi h({{R}^{2}}+{{r}^{2}}+Rr)$
Complete step by step answer:
Frustum is the slice part of a cone.
Let $R$ be the radius of Upper frustum of a right circular cone.
$r$ be the radius of Lower frustum of a right circular cone.
$h$ be the depth or height of frustum.
\[Lower\text{ }radius\text{ }of\text{ }frustum\text{ }of\text{ }cone\text{ }\left( \text{r} \right)\text{=}\dfrac{Lower\text{ }diameter\text{ }of\text{ }frustum\text{ }}{2}=\dfrac{4}{2}=2m\]
$Upper\text{ }radius\text{ }of\text{ }frustum\text{ }of\text{ }cone\text{ (R)=}\dfrac{upper\text{ }diameter\text{ }of\text{ }frustum}{2}=\dfrac{8}{2}=4m$
According to question,
Capacity of the reservoir becomes the volume of the frustum.
$\text{V}olume\text{ }of\text{ reservoir}=\dfrac{1}{3}\pi h({{R}^{2}}+{{r}^{2}}+Rr)$
$\begin{align}
& =\dfrac{1}{3}\times \pi \times 6({{4}^{2}}+{{2}^{2}}+4\times 2) \\
& =2\pi \times (16+4+8) \\
& =2\pi \times 28 \\
& =56\pi \\
& =56\times \dfrac{22}{7} \\
& =8\times 22 \\
& =176 \\
\end{align}$
Therefore, Capacity of reservoir in the shape of a frustum of a right circular cone frustum is $176\,{{m}^{3}}$.
Note: In such types of questions which involves the concept of 3D figures having knowledge about the terms related to the figures is needed. Follow up accordingly by assigning the data in the formula to get the required value.
$\text{V}olume\text{ }of\text{ }frustrum\text{ }of\text{ }cone=\dfrac{1}{3}\pi h({{R}^{2}}+{{r}^{2}}+Rr)$
Complete step by step answer:
Frustum is the slice part of a cone.
Let $R$ be the radius of Upper frustum of a right circular cone.
$r$ be the radius of Lower frustum of a right circular cone.
$h$ be the depth or height of frustum.
\[Lower\text{ }radius\text{ }of\text{ }frustum\text{ }of\text{ }cone\text{ }\left( \text{r} \right)\text{=}\dfrac{Lower\text{ }diameter\text{ }of\text{ }frustum\text{ }}{2}=\dfrac{4}{2}=2m\]
$Upper\text{ }radius\text{ }of\text{ }frustum\text{ }of\text{ }cone\text{ (R)=}\dfrac{upper\text{ }diameter\text{ }of\text{ }frustum}{2}=\dfrac{8}{2}=4m$
According to question,
Capacity of the reservoir becomes the volume of the frustum.
$\text{V}olume\text{ }of\text{ reservoir}=\dfrac{1}{3}\pi h({{R}^{2}}+{{r}^{2}}+Rr)$
$\begin{align}
& =\dfrac{1}{3}\times \pi \times 6({{4}^{2}}+{{2}^{2}}+4\times 2) \\
& =2\pi \times (16+4+8) \\
& =2\pi \times 28 \\
& =56\pi \\
& =56\times \dfrac{22}{7} \\
& =8\times 22 \\
& =176 \\
\end{align}$
Therefore, Capacity of reservoir in the shape of a frustum of a right circular cone frustum is $176\,{{m}^{3}}$.
Note: In such types of questions which involves the concept of 3D figures having knowledge about the terms related to the figures is needed. Follow up accordingly by assigning the data in the formula to get the required value.
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
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE
Select the correct plural noun from the given singular class 10 english CBSE
What organs are located on the left side of your body class 11 biology CBSE
The sum of three consecutive multiples of 11 is 363 class 7 maths CBSE
What is the z value for a 90 95 and 99 percent confidence class 11 maths CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
How many squares are there in a chess board A 1296 class 11 maths CBSE