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1 year ago

Find the lateral area and total surface area of each of the following. GEOMETRY!!! HELP PLS

Mathematics

1 answer:

AlexFokin [52]1 year ago

3 0

(a) The lateral surface area of the prism is 720 sq units and the total surface area is 752 sq units.

(b) The lateral surface area of the cone is 136π sq units and the total surface area is 200π sq units.

<h3>Lateral surface area of the prism</h3>

L.S.A = Ph

where;

P is perimeter of the base
h is height of the prism

h² = 17² - 8²

h² = 225

h = 15

L.S.A = (3 x 16) x 15 = 720 sq units

<h3>Total surface area of the prism</h3>

T.S.A = PH + 2B

T.S.A = 720 + 2(16) = 752 sq units

<h3>Lateral surface area of the cone</h3>

L.S.A = πrt

where;

t is the slant height = 17

r² = 17² - 15²

r² = 64

r = 8

L.S.A = π(8)(17) = 136π sq units

<h3>Total surface area of the cone</h3>

T.S.A = πrt + πr²

T.S.A = 136π sq units + π(8)²

T.S.A = 200π sq units

<h3> Lateral surface area of the cylinder</h3>

L.S.A = 2πrh

where;

r is the radius of the cylinder = 11
h is height of the cylinder = 11

L.S.A = 2π(11 x 11) = 242π sq units

<h3>Total surface area of the cylinder</h3>

T.S.A = 2πrh + 2πr² = 2πr(r + h)

T.S.A = 2π(11)(11 + 11)

T.S.A = 484π sq units.

Thus, the lateral surface area of the prism is 720 sq units and the total surface area is 752 sq units.

the lateral surface area of the cone is 136π sq units and the total surface area is 200π sq units.
the lateral surface area of the cylinder is 242π sq units and the total surface area is 484π sq units.

Learn more about surface area here: brainly.com/question/76387

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