Question

A semi circular sheet of diameter 28 cm is bent to form an open conical cup.Find the capacity of the conical cup (Use √3 = 1.732)​

Answer 1

As we know that the circumference of a circle is given as-

Circumference =πr

Whereas, r is the radius of circle

Diameter of circular sheet =28cm

∴ Radius of circular sheet =28/2

=14cm

Therefore,

Circumference of circular sheet =14π

When a semi-circular sheet is bent to form an open conical cup, the radius of the sheet becomes the slant height of the cup and the circumference of the sheet becomes the circumference of the base of the cone.

Slant height of cup (l)= Radius of circular sheet =14cm

Circumference of the base of cone = circumference of circular sheet =14π

Circumference of the base of cone = circumference of circular sheet =14π

Let r be the radius of the base of cone

∴2πr=14

⇒r=7cm

Let h be the height of cup.

Therefore,

l²+r²=h²

(14) ² =(7)²+h²

⇒h=√196-49=√147=7√2cm.

Now,

Capacity of cup = Volume of cone

As we know that, volume of cone is given as-

V=1/3πr²h

Therefore,

Capacity of cup =1/3×22/7×(7)²×7√3=622.4cm³

Thus the capacity of the cup is 622.4cm ³

Hence the correct answer is 622.4cm³

$\huge{\fcolorbox{a}{blue}{\fcolorbox{aqua}{aqua}{hope it helps you}}}$

Answer 2

$\bf\underline{\underline{\pink{Question:-}}}$

★ A semi-circular sheet of metalof diameter 28 cm is bent to form an open conical cup. Find the capacity of the cup.

$\bf\underline{\underline{\blue{Solution:-}}}$

When the semicircular sheet is bent into an open conical cup, the radius of the sheet becomes the slant height of the conical cup.

∴ l = 14

Circumference of the base of the cone

= length of arc ABC

= (π×14)cm = $\frac{22}{7}×14$ = 44cm

let the radius of the cone be r cm. Then,

2πr = 44 = $\frac2×{22}{7}×r$ = 44 => r = 7cm.

let the height of the cone be h cm. Then,

h² = l²–r² = (14)²–(7)² = 196–49 = 147.

∴ h = √147 = √7×7×3 = 7√3 cm

= (7×1.732)cm = 12.12cm

Capacity capacity of the conical cup

= volume of the conical cup

= ⅓πr²h

= ½ ×$\frac{22}{7}×7×7×12.12$

= (154×4.04)cm³

=622.16cm³

$\bf\underline{\underline{\green{Extra\:Formulas:-}}}$

★For a right circular cone of radius r units, height h units and land height = l units, we have

☙Slant height of the cone (l) = √h²+r² units

☙Volume of the cone = ⅓πr²h cubic units

☙Area of curved surface = (πrl) sq units = (πr√h²+r²) sq units

☙Total surface area = (area of the curved surface)+(area of the base)

= (πrl+πr²) sq units = πr(l+r) sq units