#### Mensuration Model Question Paper

10th Standard EM

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Maths

Time : 01:00:00 Hrs
Total Marks : 50
4 x 1 = 4
1. The radio of base of a one 5 cm and to height 12cm. The slant height of the cone.

(a)

12cm

(b)

17 cm

(c)

7 cm

(d)

60 cm

2. A cylinder 10 cone and have there are of a equal base and have the same height. what is the ratio of there volumes?

(a)

3:1:2

(b)

3:2:1

(c)

1:2:3

(d)

1:3:2

(a)

64

(b)

216

(c)

512

(d)

16

4. The volume of a frustum if a cone of height L and ends -radio and r1 and r2 is

(a)

$\frac{1}{3}$πh1(r12+r22+r1r2)

(b)

$\frac{1}{3}$πh(r12+r22-r1r2)

(c)

πh(r12+r22+r1r2)

(d)

πh(r12+r22-r1r2)

5. 5 x 2 = 10
6. The ratio of the volumes of two cones is 2:3. Find the ratio of their radii if the height of second cone is double the height of the first.

7. A cone of height 24 cm is made up of modeling clay. A child reshapes it in the form of a cylinder of same radius as cone. Find the height of the cylinder.

8. An aluminium sphere of radius 12 cm is melted to make a cylinder of radius 8 cm. Find the height of the cylinder.

9. If the radii of the circular ends of a conical bucket which is 45 em high are 28 em and 7 em, find the capacity of the bucket. (Use π=$\frac{22}{7}$)

10. Find the depth of a cylindrical tank of radius 28 m, if its capacity is equal to that of a rectangular tank of size 28 m x 16 m x 11 m.

11. 4 x 5 = 20
12. A hemi-spherical hollow bowl has material of volume $\frac{436\pi}{3}$cubic cm. Its external diameter is 14 cm. Find its thickness.

13. The volume of a cone is 1005$\frac{5}{7}$cu. cm. The area of its base is 201$\frac{1}{7}$sq. cm. Find the slant height of the cone.

14. What is the ratio of the volume of a cylinder, a cone, and a sphere. If each has the same diameter and same height?

15. Find the number of coins, 1.5 em is diameter and 0.2 em thick, to be melted to form' a right circular cylinder of height 10 ern and diameter 4.5 cm.

16. 2 x 8 = 16
17. xA spherical ball of iron has been melted and made into small balls. If the raidus of each smaller ball is one-fourth of the radius of the original one, how many such balls can be made?

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