Question

wooden. article. was. made. by. scooping. out.ahemisphere.from.each.end.of.asolid.cylinder.if.the.hemisphere.of.the.cylinder.is10cm.and.radius.of.the.base.is.of.3.5cm.find.the.total.surface.area.of.the.article
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Answer 1

Answer:

Step-by-step explanation:

let the original height of cylinder = 10cm

base radius of cylinder = 3.5cm

so base radius of hemisphere = 3.5cm(same as that of cylinder)

The total surface area would be the sum of curved surface area of cylinder and the surface areas of 2 hemispheres.

surface area of cylinder = 2πrh

surface area of one hemisphere = 2πr²

Answer 2

Appropriate Question:

A wooden article was made by scooping out a hemisphere from each end of a solid cylinder . If the height of the cylinder is 10 cm and its base is of radius 3.5 cm find the total surface area of the article .

Solution :

Let r be the radius of the base of the cylinder and h be the height of the cylinder.

Total surface area of the wooden article = curved surface area of the cylinder+ 2 ( surface area of the hemisphere)

$\sf{} = 2\pi \: rh + 2(\pi {r}^{2} ) = 2\pi \: r(h + 2r) \\ \\ \sf{} = (2 \times \frac{22}{7} \times 3.5 \times (10 + 2 \times 3.5) {cm}^{2} \\ \\ \sf{} =( 22 \times 17) {cm}^{2} \\ \\ \sf{} = 374 {cm}^{2}$

Therefore, total surface area of the wooden article is equals to 374 cm².

$\underline{ \underline{ \sf{ \red{ \bold{ More \: Formulas}}}}} \\ \\ \: \sf{}voume \: of \: cube \: = {a}^{3} \\ \\ \sf{}volume \: of \: cylinder = \pi {r}^{2} h \\ \\ \sf{}volume \: of \: cone = \frac{1}{3} \pi \: {r}^{2} h \\ \\ \sf{}volume \: of \: sphere \: = \frac{4}{3} \pi \: {r}^{3} \\ \\ \sf{} volume \: of \: hemisphere = \frac{2}{3} \pi {r}^{3}$