Question

A toy is in the form of a hemisphere mounted by a right circular cone . If the height of cone is 4 cm and diameter of base is 6 cm find the volume and the surface area of the toy . (take pi has 3.14 )

Answer 1

Dimensions of hemisphere,
radius, r = 6/2
= 3 cm
Dimensions of cone,
radius, r= 6/2
=3 cm
height, h = 4 cm
slant height,
l² = r² + h²
l² = 3² + 4²
l² = 9 + 16
l = √25
= 5 cm
For volume,
volume of toy = Volume of cone + volume of hemisphere
= 1/3 πr²h + 2/3 πr³
= πr² ( 1/3 h + 2/3 r)
= 3.14 × 3² ( 1/3 × 4 + 2/3 × 3)
= 3.14 × 9 ( 4/3 + 2)
= 3.14 × 9 ( 4+6/3)
= 3.14 × 9 ( 10/3)
= 3.14 × 3 × 10
= 3.14 × 30
= 94.2 cm³
For surface area,
total surface area of toy = surface area of cone + surface area of hemisphere
= πrl + 2πr²
= πr ( l + 2r)
= 3.14 × 3 ( 5 + 2(3))
= 9.42 ( 5 + 6)
= 9.42 × 11
= 103.62 cm²
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