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.

542. A tent is in the form of a cylinder surmounted by a conical top. If the height and diameter of the cylinderical part are 2.1 m and 4m respectively, and the height of the top is 2.8m, find the area of the canvas used for making the tent. Find the cost of the canvas used for making the tent. Find the cost of the canvas of the tent at the rate of Rs. 500 per m². Also, find the volume of air enclosed in the tent.

131 Views

543. A toy is in the form of a cone mounted on a hemisphere with same radius. The diameter of the base of the conical portion is 7.0 cm and the total height of the toy is 14.5 cm. Find

the volume of the toy

open square brackets Use space straight pi space equals space 22 over 7 close square brackets.

111 Views

544. An iron pillar has lower part in the form of a right circular cylinder and the upper part in the form of a right circular cone. The radius of the base of each of the cone and cylinder is 8 cm. The cylindrical part is 240 cm high and the conical part is 36 cm high. Find the weight of the pillar if 1 cm³ of iron weighs 7.5 grams.

open parentheses Take space straight pi space equals space 22 over 7 close parentheses

1227 Views

Short Answer Type

545. A bucket is made up of a metal sheet is in the form of a frustum of a cone of height 16cm with radii of its lower and upper ends at 8cm and 20cm respectively. Find the cost of the bucket, if the cost of metal sheet used is Rs. 15 per 100 cm².

93 Views

Long Answer Type

546. The height of a cone is 30 cm. A small cone is cut off at the top by a plane parallel to the base. If its volume be

1 over 27

of the volume of the given cone, at which height above the base is the section made?

449 Views

547. A hollow cone is cut by a plane parallel to the base and the upper portul is removed. If the curved surface of the remainder is

8 over 9

of the curved surface of the whole cone, find the ratio of the line-segment into which the cones altitude is divided by the plane.

1066 Views

548. If the radii of the circular ends of a conical bucket, which is 16 cm high, are 20 cm and 8 cm, find the capacity and total surface area of the bucket.

Let R and r be the radii of top of bottom circular ends of a conical bucket, respectively and ‘h’ be the height of the bucket.
∴ h =16 cm, R = 20 cm,
r = 8 cm
Capacity of the conical bucket = Volume of the bucket

$equals space 1 third πrh space left parenthesis straight R squared plus straight r squared plus Rr right parenthesis equals space 1 third straight x 22 over 7 straight x space 16 space straight x space left parenthesis 20 squared plus 8 squared plus 20 space straight x space 8 right parenthesis space cm cubed space space space space space space space space space space space space space left square bracket because space straight h space equals space 16 comma space straight R space equals space 20 space cm comma space straight r space equals space 8 space cm right square bracket equals space 1 third space straight x space 22 over 7 space straight x space 16 space left parenthesis 400 space plus space 64 space plus space 160 right parenthesis space cm cubed equals space 1 third space straight x space 22 over 7 space straight x space 16 space left parenthesis 624 right parenthesis space cm cubed equals space fraction numerator 352 space straight x space 208 over denominator 7 end fraction space cm cubed minus 73216 over 7 space cm cubed$
= 10459.428 cm³
= 10459.43 cm³
Slant height of the bucket is given by

$l italic space equals space square root of straight h squared left parenthesis straight R minus straight r right parenthesis squared end root equals space square root of left parenthesis 16 right parenthesis squared plus left parenthesis 20 minus 8 right parenthesis squared end root equals space square root of 256 plus 144 end root space cm space equals space square root of 400 space cm space equals space 20 space cm$
Total surface area of the conical bucket
= Curved surface area of the conical bucket
+ Area of the bottom
$equals space left parenthesis straight R space plus straight r right parenthesis space straight l space plus space πr squared equals space open square brackets 22 over 7 straight x left parenthesis 20 plus 8 right parenthesis space straight x space 20 plus 22 over 7 space straight x space left parenthesis 8 right parenthesis squared close square brackets space cm squared equals space 22 over 7 space left square bracket 28 space straight x space 20 space plus space 64 right square bracket space cm squared equals space 22 over 7 space straight x space left square bracket 560 space plus space 64 right square bracket space cm squared equals space 22 over 7 space straight x space left square bracket 624 right square bracket space cm squared equals space 13728 over 7 space cm squared space equals space 1961.1428 space cm squared equals space 1961.14 space cm squared$

1259 Views

549. A bucket is in the form of a frustum of a cone and holds 28.49 litres of milk. The radii of the top and bottom are 28 cm and 21 cm. Find the height of the bucket.

350 Views

Short Answer Type

550.

A bucket of height 8 cm made up of copper sheets is in the form of frustum of a right circular cone with radii of its lower ends as 3 cm and 9 cm respectively. Calculate
(i) the height of the cone of which the bucket is a part.
(ii) the volume of water which can be filled in the bucket.
(iii) the area of copper sheet required to make the bucket.

1458 Views