EASY
10th Karnataka State Board
IMPORTANT
Earn 100

The bases of a frustum of a square pyramid are of lengths 9 units and 6 units. Its slant height is 10 units. Find the total surface area of frustum of the pyramid

Important Questions on Surface Areas and Volumes

MEDIUM
10th Karnataka State Board
IMPORTANT
Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 15 - Surface Areas and Volumes>Exercise>Q 56

Two oil containers: one cylindrical and another cuboidal have the same capacity and same length. The length of a cylindrical oil container is 10 metre and the internal diameter is 6 metre. If the area of the upper rectangular surface of the cuboidal tank is 40 square metre, find its depth.

MEDIUM
10th Karnataka State Board
IMPORTANT
Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 15 - Surface Areas and Volumes>Exercise>Q 57

The height of a right circular cone is 16 cm and the radius of the base is 8 cm. The upper part is cut off by a plane through the midpoint of the axis and parallel to the base. Find the volume of the lower truncated cone.

HARD
10th Karnataka State Board
IMPORTANT
Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 15 - Surface Areas and Volumes>Exercise>Q 58
In an inverted cone of 5 cm radius and12 cm  height, a sphere is placed. If the highest point of the sphere touches the base of the cone then find the radius of the sphere. Show that the ratio of the volumes of the sphere and the cone is 40 : 81.
HARD
10th Karnataka State Board
IMPORTANT
Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 15 - Surface Areas and Volumes>Exercise>Q 59
In a right-angled triangle, the length of the sides containing the right angle are 3 cm and 4 cm. If the triangle is rotated about its hypotenuse, then two cones will be formed on the opposite side of the same base. Find their total volume.
MEDIUM
10th Karnataka State Board
IMPORTANT
Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 15 - Surface Areas and Volumes>Exercise>Q 60
A right circular cylinder of length 35 ft and radius 5 ft. From the piece, a rectangular parallelepiped of the square base is to be formed. How many cubic feet of wood will remain? How much wood was spent from the log?
EASY
10th Karnataka State Board
IMPORTANT
Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 15 - Surface Areas and Volumes>Exercise>Q 61
If a solid sphere of radius r units be melted to make a solid right circular cone of height r units, then show that the radius of the base of the cone is 2r.
EASY
10th Karnataka State Board
IMPORTANT
Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 15 - Surface Areas and Volumes>Exercise>Q 62
The height of a conical shape tower is 4 metre and the perimeter of the lower base is 11 metre. By pouring sand on the tower a cone of sand is formed whose height is 7 metre and the perimeter of the lower base is 22 metre. Find the amount of sand on the cone.
EASY
10th Karnataka State Board
IMPORTANT
Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 15 - Surface Areas and Volumes>Exercise>Q 63
There is some wheat in the form of a right circular cone whose diameter of base is 9 metre and height 3.5 metre. Find the volume of the wheat. To cover the wheat in the conical form how much canvas is required?