Question

the sum of the radius of the base and the height of a solid cylinder is 16cm and its total surface area is 352 cm square.calculate the radius of the base​

Answer 1

Answer:

3.5 cm and 12.5 cm are radius of the base and height of the cylinder respectively.

Step-by-step explanation:

Let the radius of the base of a cylinder be r

Let the height of the cylinder be h

Sum of the radius of the base and height of the cylinder = 16 cm

⇒ r + h = 16

⇒ r = 16 - h

Total surface area of the cylinder = 352 cm²

⇒ 2πr(r + h) = 352

⇒ 2 * 22/7 * (16 - h) * 16 = 352

Since r + h = 16

⇒ 2 * 22/7 * 16(16 - h) = 352

⇒ 44/7 * (256 - 16h) = 352

⇒ 256 - 16h = (352 * 7)/44

⇒ 256 - 16h = 2464/44

⇒ 256 - 16h = 56

⇒ 256 - 56 = 16h

⇒ 200 = 16h

⇒ 200/16 = h

⇒ 12.5 = h

⇒ h = 12.5 cm

Height of the cylinder = h = 12.5 cm

Radius of the base of a cylinder (r) = 16 - h = (16 - 12.5) = 3.5 cm

Therefore the 3.5 cm and 12.5 cm are radius of the base and height of the cylinder respectively.

Answer 2

Given : Sum of the radius of the base and the height of a solid cylinder is 16 cm and total surface area is 352 cm².

Find : Radius of the base of a solid cylinder.

Solution :

Sum of radius (r) and height (h) of cylinder = 16 cm

=> r + h = 16

=> r = 16 - h _____ (eq 1)

Now,

Total surface area of cylinder = 2$\pi$r (r + h)

=> 352 = 2 × $\dfrac{22}{7}$ × (16 - h) × (16 - h + h)

=> 352 = 2 × $\dfrac{22}{7}$ × (16 - h) × (16)

=> 352 = $\dfrac{44}{7}$ × (256 - 16h)

=> 352(7) = 44 × (256 - 16h)

=> 2464 = 44 × (256 - 16h)

=> $\dfrac{2464}{44}$ = 256 - 16h

=> 56 = 256 - 16h

=> 56 - 256 = 16h

=> - 200 = - 16h

=> h = 12.5

Put value of h in (eq 1)

=> r = 16 - 12.5

=> r = 3.5

Radius of solid cylinder is 3.5 cm.