Question

the total surface area of a solid right circular cylinder is 1540cm^2. if the height is four times the radius of the base, then find the height of cylinder.

Answer 1

Answer:

Height= 4r = 4×7 cm = 28 cm

Step-by-step explanation:

Let radius be r

then according to question height = 4r

here TSA=1540 cm²

total surface area of a solid right circular cylinder= 2πr(r + h)

=>1540=2πr(r + 4r)

=>1540=2πr(5r)

=>1540=10πr²

=>154/π = r²

=> r² = 49

=> r = 7

Height= 4r = 4×7 cm = 28 cm

Answer 2

Height=4× radius of the base.

⇒h=4r where r is the radius of the base

Total surface area=1540sq.cm

$2πr(r+h)=1540$

$⇒2πr(r+4r)=1540$

$⇒2 \times \frac{22}{7} ×5 {r}^{2} =1540$

$⇒ {r}^{2} = \frac{1540 \times 7}{22 \times 10} = 49$

∴r=7

Hence, the height =h=4r=4×7= 28cm