Question

Figure 7.13 shows a toy. Its lower part is a hemisphere and the upper part is a cone. Find the volume and the surface area of the toy from the measures shown in the figure.(p= 3.14)

Answer 1

$surface \: are a \: of \: toy \: \\ = surf \: area \: of \: cone + surf \: area \: of \: sphere \\ = \pi \: rl + 2\pi \: {r}^{2} \\ = \pi \: r(l + 2r) \\ = 3.14 \times 3(5 + 2 \times 3) \\ = 9.42 \times 11 \\ = 103.62 {cm}^{2}$
HENCE,
VOLUME OF TOY = 91.4 CM^3
SURFACE AREA OF TOY = 103.62CM^2

Answer 2

Hi ,

1 ) Dimensions of the cone :

radius ( r ) = 3 cm

height ( h ) = 4 cm

slant Height ( l ) = √ r² + h²

l = √ 3² + 4² = 5 cm

π = 3.14

2 ) Dimensions of the Hemisphere :

Radius ( r ) = 3 cm

3 ) Let the Surface Area of the cone = A1

Surface Area of the Hemisphere = A2

Surface Area of the toy ( A ) = A1 + A2

A = πrl + 2πr²

A = πr( l + 2r )

A = 3.14 × 3 ( 5 + 2 × 3)

A = 3.14 × 3 × 11

A = 103.62 sq cm

3 ) Volume of the toy = volume of the cone + volume of the Hemisphere

V = ( πr²h )/3 + ( 2πr³ )/3

V = ( πr²/3 ) [ h + 2r ]

V = ( 3.14 × 9 /3 ) [ 4 + 2 × 3 ]

V = 94.2 cm³

I hope this helps you.

: )