A solid consists of a conical part, a cylindrical part and a hemispherical part. All the parts have the same…

Question

A solid consists of a conical part, a cylindrical part and a hemispherical part. All the parts have the same diameter of 12 cm. The height of the cylindrical part is 15 cm and the slant height of the conical part is 10cm. (Take π = 3.142). Calculate the: (a) Height of the solid.

ScanSolve AI Tutor · Accepted Answer

Hapa kuna suluhisho la swali lako:

Ili kukokotoa urefu wa jumla wa solidi, tunahitaji kujumlisha urefu wa sehemu ya koni, urefu wa sehemu ya silinda, na urefu wa sehemu ya hemisfera.

Data iliyotolewa:

Kipenyo cha sehemu zote ( $D$ ) = $12 \text{ cm}$
Radiasi ( $r$ ) = $\frac{D}{2} = \frac{12}{2} = 6 \text{ cm}$
Urefu wa sehemu ya silinda ( $h_{cyl}$ ) = $15 \text{ cm}$
Urefu mteremko wa sehemu ya koni ( $l_{cone}$ ) = $10 \text{ cm}$

a) Urefu wa solidi.

Tafuta urefu wa sehemu ya koni ( $h_{cone}$ ) kwa kutumia theorem ya Pythagoras.
$l_{cone}^2 = r^2 + h_{cone}^2$ $10^2 = 6^2 + h_{cone}^2$ $100 = 36 + h_{cone}^2$ $h_{cone}^2 = 100 - 36$ $h_{cone}^2 = 64$ $h_{cone} = \sqrt{64}$ $h_{cone} = 8 \text{ cm}$
Tafuta urefu wa sehemu ya hemisfera ( $h_{hemi}$ ).
Urefu wa hemisfera ni sawa na radiasi yake.
$h_{hemi} = r = 6 \text{ cm}$
Kokotoa urefu wa jumla wa solidi ( $H_{total}$ ) kwa kujumlisha urefu wa sehemu zote.
$H_{total} = h_{cone} + h_{cyl} + h_{hemi}$ $H_{total} = 8 \text{ cm} + 15 \text{ cm} + 6 \text{ cm}$ $H_{total} = 29 \text{ cm}$
Urefu wa solidi ni:
$29 \text{ cm}$

A solid consists of a conical part, a cylindrical part and a hemispherical part. All the parts have the same diameter of 12 cm. The height of the cylindrical part is 15 cm and the slant height of the conical part is 10cm. (Take π = 3.142). Calculate the: (a) Height of the solid.

Answer

Step-by-step solution

Tafuta urefu wa sehemu ya koni ( $h_{cone}$ ) kwa kutumia theorem ya Pythagoras.

Tafuta urefu wa sehemu ya hemisfera ( $h_{hemi}$ ).

Kokotoa urefu wa jumla wa solidi ( $H_{total}$ ) kwa kujumlisha urefu wa sehemu zote.

Try one yourself

Still stuck on this one?

More Mathematics Questions

A solid consists of a conical part, a cylindrical part and a hemispherical part. All the parts have the same diameter of 12 cm. The height of the cylindrical part is 15 cm and the slant height of the conical part is 10cm. (Take π = 3.142). Calculate the: (a) Height of the solid.

Answer

Step-by-step solution

Tafuta urefu wa sehemu ya koni (hconeh_{cone}hcone​) kwa kutumia theorem ya Pythagoras.

Tafuta urefu wa sehemu ya hemisfera (hhemih_{hemi}hhemi​).

Kokotoa urefu wa jumla wa solidi (HtotalH_{total}Htotal​) kwa kujumlisha urefu wa sehemu zote.

Try one yourself

Still stuck on this one?

More Mathematics Questions

Tafuta urefu wa sehemu ya koni ( $h_{cone}$ ) kwa kutumia theorem ya Pythagoras.

Tafuta urefu wa sehemu ya hemisfera ( $h_{hemi}$ ).

Kokotoa urefu wa jumla wa solidi ( $H_{total}$ ) kwa kujumlisha urefu wa sehemu zote.