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Solution not provided. Ans. 7.5 m 3

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Surface Areas and Volumes

A hollow cylindrical copper pipe is 21 dm long. Its outer and inner diameters are 10 cm and 6 cm respectively. Find the volume of copper used in making the pipe.

Length of the pipe (h) = 21 dm = 210 cm Outer diameter = 10 cm.

therefore

Outer radius (R) =

10 over 2 space cm space equals space 5 space cm

because

Inner diameter = 6 cm

therefore

Inner radius (r) =

6 over 2 space cm space equals space 3 space cm

Volume of copper used in making the pipe = volume of the outer cylinder

– volume of the inner cylinder = $straight pi$ R²h – $straight pi$ r²h

$equals 22 over 7 cross times left parenthesis 5 right parenthesis squared cross times 210 minus 22 over 7 cross times left parenthesis 3 right parenthesis squared cross times 210 equals space 22 over 7 cross times 210 cross times left curly bracket left parenthesis 5 right parenthesis squared minus left parenthesis 3 right parenthesis squared right curly bracket equals space 22 over 7 cross times 210 cross times 16 equals 10560 space cm cubed.$

1778 Views

A storage tank is in the form of a cube, when full has the volume of water as 15.625 m³. If the present depth of water is 1.3 m, find the volume of water already used from the tank.

Solution not provided.

Ans. 7.5 m³

222 Views

The diameter of the base of a right circular cylinder is 28 cm and its height is 21 cm. Find its (i) curved surface area (ii) total surface area and (iii) volume.

∵ Diameter of the base (d) = 28 cm

therefore

Radius of the base (r) =

28 over 2 space c m space equals space 14 space c m

Height (h) = 21 cm
(i) Curved surface area = 2

straight pi

equals 2 cross times 22 over 7 cross times 14 cross times 21 equals 1848 space cm squared

(ii) Total surface area =

2 πr left parenthesis straight h plus straight r right parenthesis

equals 2 cross times 22 over 7 cross times 14 cross times left parenthesis 21 plus 14 right parenthesis equals 2 cross times 22 over 7 cross times 14 cross times 35 equals 3080 space cm squared

(iii) Volume =

πr squared straight h

equals 22 over 7 straight x left parenthesis 14 right parenthesis squared cross times 21 equals 12936 space cm cubed.

377 Views

A powder tin has a square base with side 8 cm and height 13 cm. Another is cylindrical with the radius of its base 7 cm and its height 15 cm.

Find the difference in their capacities. $open parentheses Use space straight pi space equals 22 over 7 close parentheses$

For a powder tin with a square base
Side of the square base = 8 cm Height = 13 cm
∴ Volume (v₁) = 8 x 8 x 13 = 832 cm³ For a cylindrical powder tin
Radius of the base (r) = 7 cm Height (h) =15 cm
∴ Volume (v₂) = $straight pi$ r²h

$equals 22 over 7 cross times left parenthesis 7 right parenthesis squared cross times 15 equals 2310 space cm cubed$
∴ Difference in their capacities = v₂ – v₁ = 2310 – 832 = 1478 cm³.

681 Views

The volume of a cylinder is 448π cm³ and height 7 cm. Find its lateral surface area and total surface area.

Let the radius of the base of the cylinder be r cm.
h = 7 cm
Volume = 448 $straight pi$ cm³

$rightwards double arrow space space space space space space space space space πr squared straight h equals 448 straight pi rightwards double arrow space space space space space space space space space straight r squared straight h equals 448 rightwards double arrow space space space space space space space space space straight r squared left parenthesis 7 right parenthesis space equals space 448 rightwards double arrow space space space space space space space space space straight r squared equals 448 over 7 rightwards double arrow space space space space space space space space straight r squared equals 64 rightwards double arrow space space space space space space space space straight r equals square root of 64 rightwards double arrow space space space space space space space space straight r equals 8 space cm$

$therefore$ Lateral surface area = 2 $straight pi$ rh

$equals 2 cross times 22 over 7 cross times 8 cross times 7 equals 352 space cm squared$
Total surface area = $2 πr left parenthesis straight h plus straight r right parenthesis$

$equals 2 cross times 22 over 7 cross times 8 cross times left parenthesis 7 plus 8 right parenthesis$
$equals 2 cross times 22 over 7 cross times 8 cross times 15 equals 5280 over 7 cm squared equals 754.28 space space cm squared.$