The figure below represents a cylindrical piece of wood, diameter 35 cm and length 100 cm. Determine the…

Question

The figure below represents a cylindrical piece of wood, diameter 35 cm and length 100 cm. Determine the surface area of the wood. (take π = 22/7)

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Haya Irene, twende na swali la kwanza la "MONDAY".

The figure below represents a cylindrical piece of wood of a diameter 35 cm and length 100 cm. Determine the surface area of the wood. (Take $\pi = \frac{22}{7}$ )

Kielelezo kinaonyesha nusu-silinda. Eneo lote la uso wa nusu-silinda linajumuisha:

Kutoka kwa swali:
Kipenyo ( $D$ ) = 35 cm
Urefu ( $L$ ) = 100 cm
Radiasi ( $r$ ) = $\frac{D}{2} = \frac{35}{2}$ cm
$\pi = \frac{22}{7}$

Kokotoa eneo la uso uliopinda wa nusu-silinda.
Eneo la uso uliopinda wa nusu-silinda = $\pi r L$
$\pi r L = \frac{22}{7} \times \frac{35}{2} \text{ cm} \times 100 \text{ cm}$ $= (11 \times 5) \times 100 \text{ cm}^2$ $= 55 \times 100 \text{ cm}^2$ $= 5500 \text{ cm}^2$
Kokotoa eneo la nusu-duara mbili (ambazo huunda duara moja kamili).
Eneo la duara moja kamili = $\pi r^2$
$\pi r^2 = \frac{22}{7} \times \left(\frac{35}{2}\right)^2 \text{ cm}^2$ $= \frac{22}{7} \times \frac{35}{2} \times \frac{35}{2} \text{ cm}^2$ $= 11 \times 5 \times \frac{35}{2} \text{ cm}^2$ $= 55 \times \frac{35}{2} \text{ cm}^2$ $= \frac{1925}{2} \text{ cm}^2$ $= 962.5 \text{ cm}^2$
Kokotoa eneo la msingi wa mstatili.
Eneo la msingi = $D \times L$
$D \times L = 35 \text{ cm} \times 100 \text{ cm}$ $= 3500 \text{ cm}^2$
Jumlisha maeneo yote kupata eneo lote la uso wa mbao.
Eneo lote la uso = Eneo la uso uliopinda + Eneo la nusu-duara mbili + Eneo la msingi
$\text{TSA} = 5500 \text{ cm}^2 + 962.5 \text{ cm}^2 + 3500 \text{ cm}^2$ $\text{TSA} = \boxed{\mathbf{9962.5 \text{ cm}^2}}$

The figure below represents a cylindrical piece of wood, diameter 35 cm and length 100 cm. Determine the surface area of the wood. (take π = 22/7)