Задачи по-английски

№ 2. The diameter of a sphere is separated into 3 parts as 1:3:2 and the perpendicular to the sections flatnesses are built through the points of separation. Find the square of the sphere's surface if the sum of the squares of the sections is 52п square sm.

№ 3. Find the square of the full surface of a cone if the perimeter of it's axis section is 16 sm. and the angle of it's flat full-scale picture is 120^o.

№ 4.The side of the grounds of a regular triangle pyramid is 4 and an angle between a rib and the grounds is 45°. Find the square of the full surface of the cone that is written into this pyramid.

Solution.

Let's find the radius of the circle that is written around tr. ABC. It' ll be=2R, R=
= R
We know that the angle DAO is 45° and DO_|(ABC). That means that the angle ADO is 45? as well. That means that AO = DO = 4. Let's find the radius of the circle that is written into the tr. ABC. Angle OAC = 30^o (half of angle BAC). Let's have a look at the triangle AOM: OM = 2. Let's have a look at the triangle DO: DM =
DM ==
S= пRl (of cone)
S = п*2*=* п
Result:* п

№ 5. The axis section of a cone is a regular triangle. A sphere is written into this cone. Find the sphere's square if the forming of the cone is 3 sm.

Solution.

Let's make a section of the cone so that tr.ABC belongs to it. Than let's draw a flat draft. Let's find the radius of the circle that is written into tr. ABC: r = S = 4пr2
r == S = 4п*= 3п