What is the volume of the ball?

Haya hapa masuluhisho ya maswali yako:

1. What is the volume of the ball?

• Step 1: Kokotoa kipenyo cha mpira. Kipimo cha kulia kwenye rula ni $5.8 \text{ cm}$. Kipimo cha kushoto kwenye rula ni $2.0 \text{ cm}$. Kipenyo $D$ ni tofauti kati ya vipimo hivi:

  $$D = 5.8 \text{ cm} - 2.0 \text{ cm} = 3.8 \text{ cm}$$

• Step 2: Kokotoa rediasi ya mpira. Rediasi $r$ ni nusu ya kipenyo:

  $$r = \frac{D}{2} = \frac{3.8 \text{ cm}}{2} = 1.9 \text{ cm}$$

• Step 3: Kokotoa ujazo wa mpira. Fomula ya ujazo wa tufe (mpira) ni $V = \frac{4}{3}\pi r^3$.

  $$V = \frac{4}{3} \times \pi \times (1.9 \text{ cm})^3$$ $$V = \frac{4}{3} \times 3.14159 \times 6.859 \text{ cm}^3$$ $$V \approx 28.73 \text{ cm}^3$$

  Ujazo wa mpira ni $\boxed{\text{28.73 cm}^3}$.

2. A solid weighs 16.5N on the surface of the moon. The force of gravity on the moon is 1.7N/kg. Determine the mass of the solid.

• Step 1: Tambua data uliyopewa. Uzito wa kitu $W = 16.5 \text{ N}$. Nguvu ya uvutano kwenye mwezi $g_{mwezi} = 1.7 \text{ N/kg}$.

• Step 2: Tumia fomula ya uzito kupata masi. Fomula inayohusisha uzito, masi, na nguvu ya uvutano ni $W = mg$. Ili kupata masi $m$, tunapanga upya fomula:

  $$m = \frac{W}{g_{mwezi}}$$ $$m = \frac{16.5 \text{ N}}{1.7 \text{ N/kg}}$$ $$m \approx 9.70588 \text{ kg}$$

  Masi ya kitu ni $\boxed{\text{9.71 kg}}$.

3. $30 \text{ cm}^3$ of a liquid X was added to $70 \text{ cm}^3$ of water and the resulting mixture had a volume slightly less than $100 \text{ cm}^3$, explain the observation.

• Step 1: Eleza hali iliyopo. Ujazo wa kioevu X ni $30 \text{ cm}^3$ na ujazo wa maji ni $70 \text{ cm}^3$. Jumla ya ujazo unaotarajiwa ni $30 \text{ cm}^3 + 70 \text{ cm}^3 = 100 \text{ cm}^3$. Hata hivyo, ujazo halisi wa mchanganyiko ni chini kidogo ya $100 \text{ cm}^3$.

• Step 2: Toa maelezo ya kisayansi. Ujazo wa mchanganyiko kuwa chini ya jumla ya ujazo wa vinywaji vilivyochanganywa unaelezewa na ukweli kwamba kuna nafasi kati ya chembechembe (molekuli) za vinywaji. Wakati kioevu X na maji vinapochanganywa, chembechembe ndogo za kioevu kimoja huingia na kujaza nafasi zilizo wazi kati ya chembechembe kubwa za kioevu kingine. Hii inasababisha mchanganyiko kuwa na ujazo mdogo kuliko jumla ya ujazo wa vinywaji vilivyochanganywa kando.