Question

У кулю, радіус якої дорівнює 5 см, вписано циліндр, твірна якого дорівнює 8 см. Знайти площу бічної поверхні циліндра.

Answer 1

Ответ:

48π

Объяснение:

діагональ осьового перерізу циліндра 2*5=10

діаметр основи циліндра

$\sqrt{ {10}^{2} - {8}^{2} } = \sqrt{36} = 6$

площа бічної поверхні циліндра π*d*h = 6*8*π=48π

Answer 2

#### Problem Analysis We are given a sphere with a radius of 5 cm, and a cylinder inscribed within it, with a height (or generatrix) of 8 cm. We need to find the lateral surface area of the cylinder. #### Solution To find the lateral surface area of the cylinder, we need to calculate the circumference of the base and multiply it by the height of the cylinder. The circumference of the base of the cylinder is equal to the circumference of the sphere, which is equal to the circumference of a circle with a radius of 5 cm. The formula for the circumference of a circle is **C = 2πr**, where **C** is the circumference and **r** is the radius. Substituting the value of the radius (5 cm) into the formula, we get: **C = 2π(5) = 10π cm**. Now, we can calculate the lateral surface area of the cylinder by multiplying the circumference of the base by the height of the cylinder. The formula for the lateral surface area of a cylinder is **A = Ch**, where **A** is the lateral surface area, **C** is the circumference of the base, and **h** is the height of the cylinder. Substituting the values of the circumference (10π cm) and the height (8 cm) into the formula, we get: **A = (10π)(8) = 80π cm²**. Therefore, the lateral surface area of the cylinder is **80π cm²**. #### Answer The lateral surface area of the cylinder inscribed within the sphere, with a radius of 5 cm and a height of 8 cm, is **80π cm²**.