a toy is in form of cone mounyed ona hemisphere the diameter of box of cone is 10 cm and height is 12 cm calculate TSA
Answers
Answer:
The volume of the toy is 231 cm cube.
Total surface area of the toy is 203.5 cm square.
Step-by-step explanation:
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.
$$\begin{lgathered}l=\sqrt{r^2+h^2}\\l=\sqrt{3.5^2+11^2}\\l=\sqrt{133.25}\\l=11.5\end{lgathered}$$
Total surface of the toy = TSA(cone)+ TSA(hemisphere)
$$TSA=\pi rl+2\pi r^2$$
$$TSA=\pi r(l+2r)$$
$$TSA=\frac{22}{7}\times 3.5(11.5+2(3.5))$$
$$TSA=\frac{22}{7}\times 3.5\times 18.5$$
$$TSA=203.5cm^2$$
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Total surface area of the toy is 203.5 cm square
Answer:
The formula for the total surface area of a right cone is T. S. A=πrl+πr2 .
Step-by-step explanation:
22/7×5×12+22/7(5)^2