Surface Areas and Volumes Chapter 12 Class 10 Mathematics PYQs
Q1:
A golf ball is spherical with about 300 500 dimples that help increase its velocity while in play. Golf balls are traditionally white but available in colours also. In the given figure, a golf ball has diameter 4·2 cm and the surface has 315 dimples (hemi-spherical) of radius 2 mm. Based on the above, answer the following questions : (i) Find the surface area of one such dimple. (ii) Find the volume of the material dug out to make one dimple. (iii) (a) Find the total surface area exposed to the surroundings. OR (b) Find the volume of the golf ball.
CBSE [2023]
HardQ2:
From a solid cylinder of height 20 cm and diameter 12 cm, a conical cavity of height 8 cm and radius 6 cm is hallowed out. Find the total surface area of the remaining solid.
CBSE [2023]
MediumQ3:
A student was asked to make a model shaped like a cylinder with two cones attached to its ends by using a thin aluminium sheet. The diameter of the model is 3 cm and its total length is 12 cm. If each cone has a height of 2 cm, find the volume of air contained in the model.
CBSE [2023]
EasyQ4:
In a coffee shop, coffee is served in two types of cups. One is cylindrical in shape with diameter 7 cm and height 14 cm and the other is hemispherical with diameter 21 cm. Based on the above, answer the following questions : (i) Find the area of the base of the cylindrical cup. (ii) (a) What is the capacity of the hemispherical cup ? OR (b) Find the capacity of the cylindrical cup. (iii) What is the curved surface area of the cylindrical cup ?
CBSE [2023]
MediumQ5:
An empty cone is of radius 3 cm and height 12 cm. Ice-cream is filled in it so that lower part of the cone which is \(\left(\frac{1}{6}\right)^{\text{th}}\) of the volume of the cone is unfilled but hemisphere is formed on the top. Find the volume of the ice-cream. (Take π = 3.14)
CBSE [2023]
MediumQ6:
Khurja pottery is traditional Indian pottery work which has attracted Indians as well as foreigners with a variety of tea-sets, crockery and ceramic tile works. Following are the few pottery objects of Khurja. Students found the shapes of the objects very interesting and they could easily relate them with mathematical shapes viz sphere, hemisphere, cylinder etc. Maths teacher who was accompanying the students asked the following questions : (a) The internal radius of hemispherical bowl (filled completely with water in I is 9 cm and radius and height of the cylindrical jar in II is 1.5 cm and 4 cm respectively. If the hemispherical bowl is to be empties in cylindrical jars, then how many cylindrical jars are required ? (b) If in the cylindrical jar full of water, a conical funnel of same height and same diameter is immersed, then how much water will flow out of the jar ?
CBSE [2022]
EasyQ7:
The largest sphere is carved out of a solid cube of side 21 cm. Find the volume of the sphere.
CBSE [2022]
EasyQ8:
John planned a birthday party for his younger sister with his friends. They decided to make some birthday caps by themselves and to buy a cake from a bakery shop. For these two items, they decided the following dimensions : Cake : Cylindrical shape with diameter 24 cm and height 14 cm. Cap : Conical shape with base circumference 44 cm and height 24 cm. Based on the above information, answer the following questions : (a) How many square cm paper would be used to make 4 such caps ? (b) The bakery shop sells cakes by weight (0·5 kg, 1 kg, 1·5 kg, etc.). To have the required dimensions, how much cake should they order, if 650 cm3 equals 100 g of cake ?
CBSE [2022]
MediumQ9:
Three cubes of side 6 cm each, are joined as shown in the figure. Find the total surface area of the resulting cuboid.
CBSE [2022]
EasyQ10:
150 spherical marbles, each of diameter 1.4 cm, are dropped in a cylindrical vessel of diameter 7 cm containing some water, and are completely immersed in water. Find the rise in the level of water in the cylindrical vessel.
CBSE [2022]
MediumQ11:
