Construct a circle that touches points ABC. What is the radius of the circle? (3mks)

Question

ScanSolve AI Tutor · Accepted Answer

Ili kukokotoa ujazo wa frustum, tutatoa ujazo wa koni ndogo iliyokatwa kutoka kwenye ujazo wa koni kubwa ya asili.

Kutokana na maelezo:

Urefu wa frustum ( $H_f$ ) = $40 \text{ cm}$
Radiasi kubwa ( $R$ ) = $30 \text{ cm}$
Radiasi ndogo ( $r$ ) = $7 \text{ cm}$
Urefu wa koni ndogo iliyokatwa ( $h$ ) = $10 \text{ cm}$

Hii inamaanisha:

Koni kubwa ina radiasi $R = 30 \text{ cm}$ na urefu jumla $H = H_f + h = 40 \text{ cm} + 10 \text{ cm} = 50 \text{ cm}$ .
Koni ndogo ina radiasi $r = 7 \text{ cm}$ na urefu $h = 10 \text{ cm}$ .

Fomula ya ujazo wa koni ni $V = \frac{1}{3} \pi r^2 h$ . Tutatumia $\pi = \frac{22}{7}$ .

Kokotoa ujazo wa koni kubwa.
Ujazo wa koni kubwa ( $V_L$ ) hutumia radiasi $R = 30 \text{ cm}$ na urefu $H = 50 \text{ cm}$ .
$V_L = \frac{1}{3} \pi R^2 H$ $V_L = \frac{1}{3} \times \frac{22}{7} \times (30 \text{ cm})^2 \times (50 \text{ cm})$ $V_L = \frac{1}{3} \times \frac{22}{7} \times 900 \text{ cm}^2 \times 50 \text{ cm}$ $V_L = \frac{22}{7} \times 300 \text{ cm}^2 \times 50 \text{ cm}$ $V_L = \frac{22}{7} \times 15000 \text{ cm}^3$ $V_L = \frac{330000}{7} \text{ cm}^3$ $V_L \approx 47142.8571 \text{ cm}^3$
Kokotoa ujazo wa koni ndogo iliyokatwa.
Ujazo wa koni ndogo ( $V_S$ ) hutumia radiasi $r = 7 \text{ cm}$ na urefu $h = 10 \text{ cm}$ .
$V_S = \frac{1}{3} \pi r^2 h$ $V_S = \frac{1}{3} \times \frac{22}{7} \times (7 \text{ cm})^2 \times (10 \text{ cm})$ $V_S = \frac{1}{3} \times \frac{22}{7} \times 49 \text{ cm}^2 \times 10 \text{ cm}$ $V_S = \frac{1}{3} \times 22 \times 7 \text{ cm}^2 \times 10 \text{ cm}$ $V_S = \frac{1540}{3} \text{ cm}^3$ $V_S \approx 513.3333 \text{ cm}^3$
Kokotoa ujazo wa frustum.
Ujazo wa frustum ( $V_f$ ) ni tofauti kati ya ujazo wa koni kubwa na ujazo wa koni ndogo.
$V_f = V_L - V_S$ $V_f = \frac{330000}{7} \text{ cm}^3 - \frac{1540}{3} \text{ cm}^3$
Ili kutoa, tunahitaji kupata kigawo cha kawaida, ambacho ni 21.
$V_f = \frac{330000 \times 3}{21} \text{ cm}^3 - \frac{1540 \times 7}{21} \text{ cm}^3$ $V_f = \frac{990000}{21} \text{ cm}^3 - \frac{10780}{21} \text{ cm}^3$ $V_f = \frac{990000 - 10780}{21} \text{ cm}^3$ $V_f = \frac{979220}{21} \text{ cm}^3$ $V_f \approx 46629.5238 \text{ cm}^3$
Ukizungusha hadi sehemu mbili za desimali:
$V_f \approx 46629.52 \text{ cm}^3$
Ujazo wa frustum ni:
$\text{46629.52 cm}^3$

Construct a circle that touches points ABC. What is the radius of the circle? (3mks)

Answer

Step-by-step solution

Kokotoa ujazo wa koni kubwa.

Kokotoa ujazo wa koni ndogo iliyokatwa.

Kokotoa ujazo wa frustum.

Try one yourself

Still stuck on this one?

More Mathematics Questions