Question

A right circular solid cylinder has radius 7cm and height 24cm. A conical cavity of same dimensions is carved out of the cylinder. Then the sum of the areas, in square centimeters, of the inner and outer surfaces of the remaining solid is?

Answer 1

Solution:

Radius if Cylinder r = 7 cm

Height h = 24 cm

Total Surface area of Cylinder =
$2\pi \: r \: h + 2\pi \: {r}^{2} \\ \\ = \frac{44}{7} \times 7 \times 24 + \frac{44}{7} \times 49 \\ \\ = 1056 + 308 \\ \\ = 1364 \: {cm}^{2}$
A conical cavity of r= 7 cm and height = 24 cm is carved out

Total surface area of Cone
$= \pi \: r \: l + \pi \: {r}^{2} \\ \\ l = \sqrt{576 + 49} \\ \\ l = 25 \: cm \\ \\ TSA \: = \frac{22}{7} \times 7 \times 25 + \frac{22}{7} \times 49 \\ \\ = 22 \times 25 + 22 \times 7 \\ \\ = 550 + 154 \\ \\ = 704 {cm}^{2}$

Sum of outer and inner surface area of remaining solid = CSA of Cylinder + CSA of Cone+Area of Circle

$1056+550 +154 \\ \\ = 1760\: sq - cm$

Answer 2

Answer:

1760 cm²

Step-by-step explanation:

Find the surface area of the cylinder without the top:

Surface area = πr² + 2πrh

Surface area = π(7)² + 2π(7)(24) = 1210 cm²

Find the slanted height of the cone:

a² + b² = c²

7² + 24² = c

c² = 625

c = √625

c = 25 cm

Find the lateral surface area of the cone:

Lateral surface area =πrl

Lateral surface area =π(7)(25) = 550 cm²

Find the sum of the inner and outer surface:

Total surface are = 1210 + 550 = 1760 cm²

Answer: 1760 cm²