Question

the total surface area of a cylinder is 2464 sq.cm the height and radius of the cylinder are equal. find the radius of the base of the cylinder​

Answer 1

Step-by-step explanation:

THE HEIGTH AND THE RADIUS OF THE CYLINDER IS EQUAL. LET THE HEIGHT AND THE RADIUS BE x. THEREFORE, THE HEIGHT AND THE RADIUS OF THE CYLINDER IS 14 CM.

Answer 2

Given :

• Total surface area of cylinder = 2464 cm²
• Height and radius of the cylinder are equal.

To find :

• Radius of the base of the cylinder

Concept :

Formula of Total surface area of cylinder :-

• Total surface area of cylinder = 2πr(h + r)

where,

• Take π = 22/7
• r = radius of the cylinder
• h = height of the cylinder

Solution :

• Radius = Height = a

Using formula,

• Total surface area of cylinder = 2πr(h + r)

Substituting the given values,

$\\ \dashrightarrow \sf \quad 2464 = 2 \times \dfrac{22}{7} \times a(a + a)$

$\\ \dashrightarrow \sf \quad 2464 = \dfrac{44}{7}a(a + a)$

$\\ \dashrightarrow \sf \quad 2464 = \dfrac{44}{7}a(2a)$

$\\ \dashrightarrow \sf \quad 2464 = \dfrac{88}{7}a^{2}$

$\\ \dashrightarrow \sf \quad 2464 \times \dfrac{7}{88} = a^{2}$

$\\ \dashrightarrow \sf \quad 28 \times 7 = a^{2}$

$\\ \dashrightarrow \sf \quad \sqrt{28 \times 7} = a$

$\\ \dashrightarrow \sf \quad \sqrt{7 \times 2 \times 2 \times 7} = a$

$\\ \dashrightarrow \sf \quad \pm \: 7 \times2 \: Reject - ve= a$

$\\ \dashrightarrow \sf \quad 14= a$

The value of a = 14.

Radius = Height = 14 cm.

∴ Radius of the base of the cylinder = 14 cm.

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Verification :

Substitute the value of radius and height in the formula of TSA of cylinder.

$\\ \dashrightarrow \sf \quad TSA = 2 \times \dfrac{22}{7} \times 14(14 + 14)$

$\\ \dashrightarrow \sf \quad TSA = 2 \times \dfrac{22}{7} \times 14(28)$

$\\ \dashrightarrow \sf \quad TSA = 2 \times \dfrac{22}{ \not7} \times \not14(28)$

$\\ \dashrightarrow \sf \quad TSA = 2 \times 22 \times 2(28)$

$\\ \dashrightarrow \sf \quad TSA = 2464 \: {cm}^{2}$

Hence, verified.