sol.
2. (i) A toy is in the form of a cone mounted on a hemisphere of diameter 7
cm. The total height of the toy is 14.5 cm. Find the total surface area of the
toy.
Answers
Answer:
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Answer:
Given : A toy is in the form of cone mounted on the hemisphere of diameter 7 cm . the total height of the tower is 14.5 cm.
To find : The volume and total surface area of the toy?
Solution :
Hemisphere of diameter 7 cm
Radius is r=\frac{7}{2}=3.5r=
2
7
=3.5
Height of the toy= 14.5
Height of the cone= 14.5 - 3.5=11cm
Height of the hemisphere=3.5cm
According to question,
Volume of the toy = V(cone)+ V(hemisphere)
V=\frac{1}{3}\pi r^2 h+\frac{4}{3}\pi r^3V=
3
1
πr
2
h+
3
4
πr
3
V=\frac{1}{3}\pi r^2[h+2r]V=
3
1
πr
2
[h+2r]
V=\frac{1}{3}\times \frac{22}{7}\times (3.5)^2[11+2(3.5)]V=
3
1
×
7
22
×(3.5)
2
[11+2(3.5)]
V=\frac{1}{3}\times \frac{22}{7}\times 3.5\times 3.5\times 18V=
3
1
×
7
22
×3.5×3.5×18
V=231V=231
The volume of the toy is 231 cm cube.
\begin{gathered}l=\sqrt{r^2+h^2}\\l=\sqrt{3.5^2+11^2}\\l=\sqrt{133.25}\\l=11.5\end{gathered}
l=
r
2
+h
2
l=
3.5
2
+11
2
l=
133.25
l=11.5
Total surface of the toy = TSA(cone)+ TSA(hemisphere)
TSA=\pi rl+2\pi r^2TSA=πrl+2πr
2
TSA=\pi r(l+2r)TSA=πr(l+2r)
TSA=\frac{22}{7}\times 3.5(11.5+2(3.5))TSA=
7
22
×3.5(11.5+2(3.5))
TSA=\frac{22}{7}\times 3.5\times 18.5TSA=
7
22
×3.5×18.5
TSA=203.5cm^2TSA=203.5cm
2
Total surface area of the toy is 203.5 cm square.