Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.

It costs र 2200 to paint the inner curved surface of a cylindrical vessel 10 m deep. If the cost of painting is at the rate of र 20 per m², find
(i) inner curved surface area of the vessel,
(ii) radius of the base,
(iii) capacity of the vessel.

121 Views

156. The capacity of a closed cylindrical vessel of height 1 m is 15.4 litres. How many square metres of metal sheet would be needed to make it?

378 Views

157. A lead pencil consists of a cylinder of wood with a solid cylinder of graphite filled in the interior. The diameter of the pencil is 7 mm and the diameter of the graphite is 1 mm. If the length of the pencil is 14 cm, find the volume of the wood and that of the graphite.

For solid cylinder of graphite
Diameter = 1 mm

$therefore$ Radius (r) = $1 half space mm$

Length of the pencil (h) = 14 cm = 140 mm

∴ Volume of the graphite = $straight pi$ r²h

$equals 22 over 7 cross times open parentheses 1 half close parentheses squared cross times 140 equals 110 space mm cubed equals fraction numerator 110 over denominator 10 cross times 10 cross times 10 end fraction space cm cubed equals 0.11 space cm cubed$

For cylinder of wood
Diameter = 7 mm

$therefore space space$ Radius (R) = $7 over 2$ mm
Length of the pencil (h) = 14 cm = 140 mm
$therefore$ Volume of the wood

$equals straight pi left parenthesis straight R squared minus straight r squared right parenthesis straight h equals 22 over 7 open curly brackets open parentheses 7 over 2 close parentheses squared minus open parentheses 1 half close parentheses squared close curly brackets space 140 equals space 5280 space mm cubed equals fraction numerator 5280 over denominator 10 cross times 10 cross times 10 end fraction space cm cubed equals 5.28 space cm cubed$

530 Views

158.

A patient in a hospital is given soup daily in a cylindrical bowl of diameter 7 cm. If the bowl is filled with soup to a height of 4 cm, how much soup the hospital has to prepare daily to serve 250 patients?

206 Views

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

3174 Views

160. 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.

377 Views

Previous Year Papers

Test Series

Test Yourself

Surface Areas and Volumes

Short Answer Type

157. A lead pencil consists of a cylinder of wood with a solid cylinder of graphite filled in the interior. The diameter of the pencil is 7 mm and the diameter of the graphite is 1 mm. If the length of the pencil is 14 cm, find the volume of the wood and that of the graphite.