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Mathematics Grade 10 Unit 6: Solid Figures
national exam questions have come from this unit. It runs 53 pages; one careful study pass takes about 4.0 hours, and its difficulty is easier among Mathematics units. Each section below lists the questions set from it, with the year, and opens the page that teaches it.
6.2 Pyramids, cones and Spheres · read p. 294
- 2018 E.C., Q58 – A spherical ball has diameter 30cm. What is its surface area (in )?
- 2017 E.C., Q11 – What is the surface area (in cm$^2$) of leather material required to make a spherical shape ball of radius 25cm?
- 2016 E.C., Q44 – What is the total surface area of a regular square pyramid with slant height $8\text{cm}$ and base area $25\,\text{cm}^2$?
- 2016 E.C., Q9 – Which of the following is the approximate surface area of the bases of a regular pentagonal prism of radius 6 cm? (Given values: sin72° ≈ 0.3, cos72° ≈ 0.95)
- 2014 E.C., Q14 – Which one of the following points is, inside the sphere with equation $x^2+y^2+z^2=5$?
- 2014 E.C., Q3 – What is the surface area of a sphere with radius 6 cm?
- 2013 E.C., Q4 – Which of the following defines the equation of a sphere whose center is at $(0, -1, 2)$ and radius 6 units?
6.3 Frustum of pyramids and cones · read p. 321
- 2017 E.C., Q23 – If a square pyramid has a base side of 6 cm long and its lateral faces are equilateral triangles, then what is its volume (in $\text{cm}^3$)?
- 2017 E.C., Q20 – Which of the following statements defines frustum of a pyramid?
- 2017 E.C., Q45 – What is the total surface area (in cm ) of the cylinder whose radius is 2cm and height is 7cm?
- 2017 E.C., Q14 – What is the total surface area (in $\text{cm}^2$) of the cylinder whose radius is 2 cm and height is 7 cm?
- 2016 E.C., Q3 – The altitude of a frustum of a regular square pyramid is 9 cm. What is the volume of the frustum if the side length of the upper base is 6 cm and the side length of the lower base is 10 cm? 3 3
- 2015 E.C., Q15 – The object shown in the figure below is made of wood. Its top cover is a solid hemisphere and its bottom is a cylindrical part of base diameter 6cm and height of 12cm. From the bottom of the cylindrical part of height 8c
- 2015 E.C., Q12 – Which one of the following statements defines frustum of a pyramid?
- 2015 E.C., Q11 – A frustum of a cone is formed from a right circular cone of height 15cm. If the base radii of the frustum are 2cm and 3cm, where the height from the smaller base to the vertex is 4cm, what is the volume of the frustum of
- 2014 E.C., Q48 – A carpenter wants to design a closed box that has a square base and total surface area of 54 cm 2 . What is the maximum volume that can be constructed with the given total surface area?
- 2014 E.C., Q5 – If the volume of a right circular cone is 64π cm 3 and the diameter of its base is 8 cm, what is the height of the cone?
6.4 Surface areas and volumes of composed solids · read p. 331
Not asked in a national paper yet.
6.5 Applications · read p. 336
- 2015 E.C., Q45 – Water is running into a canonical tank, which is pointed down at a constant rate of $6\pi\,\text{cm}^3/\text{sec}$. The cone has a height of 10 cm and a base radius of 5 cm, then how fast is the water level rising when t