1. Drag and drop an answer to each box to correctly complete the derivation of a formula for the area of a sector of a circle.2. Drag and drop an answer to each box to correctly explain the derivation of the formula for the volume of a pyramid.3. The equation for a circle is ​x2−8x+y2−2y−8=0​ . What is the equation of the circle in standard form?

Answer:- Central angle , Ф/2π , A = Ф/2 r²The ratio is 1/3 , V = 1/3 BhThe equation of the circle in standard form is (x - 4)² + (k - 1)² = 25Step-by-step explanation:* Lets revise the rules of the area of the sector of a circle- The area of the sector which has a central angle Ф° is   (Ф°/360°) × πr², where 360° is the measure of the circle and r is   the radius of the circle- The area of the sector which has a central angle Ф radians is   (1/2) r²Ф* Lets complete the missing in the 1st picture- The ratio of the sector's area A to the circle's area is equal to the   ratio of the central angle to the measure of a full rotation of the circle- A full rotation of a circle is 2π. This proportion can written as  A/πr² = Ф/2π- Multiply both sides by πr² to get A = Ф/2 r² where Ф is the measure  of the central angle and r is the radius of the circle* Lets revise the rules of the volume of the prism and the volume  of the pyramid, where they have the same base and height- The volume of the prism = area of the base × its height- The volume of the pyramid = 1/3 × area of the base × its height- From them the ratio of the volume of the pyramid to the volume  of the prism is 1/3- The formula of the volume of the prism is V = Bh, where B is the   area of the base and h is the height, the formula of the volume   of the pyramid is V = 1/3 Bh* Lets revise the standard form of the equation of a circle with  center (h , k) and radius r- The equation is: (x - h)² + (y - k)² = r²∴ x² - 2hx + h² + y² - 2ky + k² - r² = 0∵ x² - 8x + y² - 2y - 8 = 0- Lets equate the two equation∴ x² - 2hx + h² + y² - 2ky + k² - r² = x² - 8x + y² - 2y - 8 = 0∵ -2h = -8 ⇒ ÷ -2∴ h = 4∵ -2k = -2 ⇒ ÷ -2∴ k = 1∵ h² + k² - r² = -8∴ (4)² + (1)² - r² = -8∴ 16 + 1 - r² = -8∴ 17 - r² = -8 ⇒ subtract 17 from both sides∴ -r² = -15 × -1∴ r² = 25* Substitute the values of h , k , r in the equation of the standard  form of the circle∴ (x - 4)² + (k - 1)² = 25 * The equation of the circle in standard form is (x - 4)² + (k - 1)² = 25