the diameter of a metallic ball is 5.6cm what is the mass of the ball ,if the density of the metal is 18 g per cm√3
Answers
Answer:
Height of cane is 9.99 cm.
Volume of cane is 6153.84 cm³.
Step-by-step explanation:
Given:-
Curved surface area of a powder cane is 879.3 cm².
Diameter of the base is 28 cm.
To find:-
Height of cane.
Volume of cane.
Solution:-
Radius = Diameter/2
= 28/2
= 14
Radius of cane is 14 cm.
Let, Height of cane be h.
We know the shape of cane is cylinder.
\boxed{\sf \bold{Curved \: surface \: area \: of \: cylinder = 2 \pi r h}}
Curvedsurfaceareaofcylinder=2πrh
Where,
r is radius and h is height of cylinder.
Put r, h and curved surface area in formula :
\begin{gathered} \sf \longrightarrow 879.2 = 2\times \dfrac{22}{\cancel{7}} \times \cancel{14} \times h \\ \\ \end{gathered}
⟶879.2=2×
7
22
×
14
×h
\begin{gathered} \sf \longrightarrow 879.2 = 44 \times 2 \times h \\ \\ \end{gathered}
⟶879.2=44×2×h
\begin{gathered} \sf \longrightarrow 879.2 = 88 \times h \\ \\ \end{gathered}
⟶879.2=88×h
\begin{gathered} \sf \longrightarrow h = \dfrac{879.2}{88} \\ \\ \end{gathered}
⟶h=
88
879.2
\begin{gathered} \longrightarrow \purple{ \boxed{\sf \bold{h = 9.99}}\star} \\ \\ \end{gathered}
⟶
h=9.99
⋆
Height of cane is 9.99 cm.
\begin{gathered} \\ \end{gathered}
\boxed{\sf \bold{Volume \: of \: cylinder = \pi r^{2} h}}
Volumeofcylinder=πr
2
h
Put r and h in formula :
\begin{gathered} \sf \longrightarrow \dfrac{22}{7} \times (14)^{2} \times 9.99 \\ \\ \end{gathered}
⟶
7
22
×(14)
2
×9.99
\begin{gathered} \sf \longrightarrow \dfrac{22}{\cancel{7}} \times \cancel{14} \times 14 \times 9.99 \\ \\ \end{gathered}
⟶
7
22
×
14
×14×9.99
\begin{gathered} \sf \longrightarrow 22 \times 2 \times 14 \times 9.99 \\ \\ \end{gathered}
⟶22×2×14×9.99
\begin{gathered} \sf \longrightarrow 44 \times 14 \times 9.99 \\ \\ \end{gathered}
⟶44×14×9.99
\begin{gathered} \longrightarrow \red{\boxed{\sf \bold{6153.84}}\star} \\ \\ \end{gathered}
⟶
6153.84
⋆
Therefore,
Volume of cane is 6153.84 cm³.
Radius (r 1 ) of hemisphere =4.2 cm
Radius (r
2
) of cylinder =6 cm
Height (h) = ?
The object fromed by recasting the hemisphere will be same in volume.
So, Volume of sphere = Volume of cylinder
3
4
πr
1
3
=πr
2
2
h
⟹
3
4
π×(4.2)
3
=π(6)
2
h
⟹
3 × 36
4.2×4.2×4.2=h
h=(1.4)³ =2.74 cm
Therefore, the height of cylinder so formed will be 2.74 cm.