A toy is made in the form of hemisphere surmounted by a right cone whose circular base is joined with the plane surface of the hemisphere. The radius of the base of the cone is 7 cm. and its volume is 3/2 of the hemisphere. Calculate the height of the cone and the surface area of the toy correct to 2 places of decimal [Take π = 3 1/7].
Answers
Answer:
Volume of the hemisphere = 2/3πr 3
Vol. of cone=3/2x2/3πr ^3= πr^3
= πx7^3=343πcm3(data given)
343π = Vol. of cone=I/3πr ^2 =
1/3πx7^2 xh
h=343πx3/πx49=21cm
height of the CONE=21cm
slant height of the cone: I=v.r^2+h^2
= v7^2+21^2 =v 49+441 = V 500
10v5cm
surface area of the TOY
2πr ^2+πrl=2x22x7x7/7+22x7x10V5/7
v5=2.236
308+491.92 = 799.92cm2
SA of TOY=799.92cm2
πrl+2πr^2 =
-
Answer:
Step-by-step explanation:
Radius of the cone and hemisphere = 7 cm
Let the height of cone be = h cm
Volume of cone = (1/3)πr²h
Volume of hemisphere = (2/3)πr³
Thus, on solving -
= (1/3)πr²h = (3/2) ×(2/3)πr³
= h = 3r
= 3×7
= 21
Surface area - Slant height, l = √(21)² +(7)²
= 7√10 cm
= 22.1
Total surface area = Surface area of cone + Hemisphere
= πrl + 2πr²
= (22/7) × 7 ×22.1 + 2 × 22/7 × 7²
= 486.86 +308
= 794.86
Thus the surface area of the toy is - 794.86 cm²