Question

find the volume curved surface area and total surface area of the cylinder whose height and radius of the base are 28 cm and 3 cm respectively​

Answer 1

Answer:

(1) Volume = 682 cm³

(2) Curved Surface Area = 528 cm²

(3) Total Surface Area = 584.57 cm²

Step-by-step explanation:

Information provided to us-

1. Radius of the base of the cylinder = 3 cm

2. Height of the cylinder = 28 cm

Let us denote radius of the base of the cylinder by 'r' and the height of the cylinder by 'h'.

Hence,

r = 3 cm

h = 28 cm

We know that, volume of cylinder is,

$\pi \: r {}^{2} h$

Substituting the values in the above formula,

$\pi {(3)}^{2} \times 28 \\ = 9\pi \times 28 \\ = 252\pi \\ = 252 \times \frac{22}{7} \\ \\ = 31 \times 22 \\ = 682 \: cm {}^{3}$

We know that, the curved surface area of a cylinder is,

$2\pi \: rh$

Substituting the values in the above formula,

$2\pi \times 3 \times 28 \\ = 2 \times \frac{22}{7} \times 3 \times 28 \\ \\ = 44 \times 3 \times 4 \\ = 44 \times 12 \\ = 528 \: cm {}^{2}$

We know that, the total surface area of a cylinder is,

$2\pi \: r(r + h)$

Substituting the values in the above formula,

$2\pi \times 3(3 + 28) \\ = 2\pi \times 3 \times 31 \\ = 2\pi \times 93 \\ = 186\pi \\ = 186 \times \frac{22}{7} \\ \\ = \frac{4092}{7} \\ \\ = 584.57 \: cm {}^{2}$